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Michela ELEUTERI

Professore Ordinario
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Matematica

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Pubblicazioni

2023 - Aree e volumi: si può sempre misurare? [Articolo su rivista]
Benassi, Carlo; Eleuteri, Michela; Lussardi, Luca
abstract

2023 - Asymptotic analysis of a family of non-local functionals on sets [Articolo su rivista]
Eleuteri, M; Lussardi, L; Torricelli, A
abstract

We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first compute the pointwise limit and we obtain a lower estimate on more regulars sets. Finally, some examples are discussed.

2023 - La retta di regressione incontra l'Intelligenza Artificiale [Relazione in Atti di Convegno]
Ferri, Caterina; Benassi, Carlo; Eleuteri, Michela; Monari, Pietro
abstract

2023 - Lipschitz regularity of minimizers of variational integrals with variable exponents [Articolo su rivista]
Eleuteri, Michela; Passarelli di Napoli, Antonia
abstract

2023 - Minimizers of abstract generalized Orlicz-bounded variation energy [Articolo su rivista]
Eleuteri, M.; Harjulehto, P.; Hasto, P.
abstract

A way to measure the lower growth rate of phi : Omega x [0, infinity) -> [0, infinity) is to require t (sic) phi (x, t)t(-r) to be increasing in (0, infinity). If this condition holds with r = 1, theninf (u is an element of f+W1,phi (Omega)) integral(Omega) phi(x, vertical bar del u vertical bar) dxwith boundary values f is an element of W-1,W-phi (Omega) does not necessarily have a minimizer. However, if phi is replaced by phi(p), then the growth condition holds with r = p > 1 and thus (under some additional conditions) the corresponding energy integral has a minimizer. We show that a sequence (u(p)) of such minimizers converges when p -> 1(+) in a suitable BV-type space involving generalized Orlicz growth and obtain the Gamma-convergence of functionals with fixed boundary values and of functionals with fidelity terms.

2022 - A scuola di Intelligenza Artificiale [Relazione in Atti di Convegno]
Benassi, Carlo; Eleuteri, Michela; Ferri, Caterina; Monari, Pietro
abstract

2022 - Local Lipschitz continuity for energy integrals with slow growth [Articolo su rivista]
Eleuteri, M.; Marcellini, P.; Mascolo, E.; Perrotta, S.
abstract

We consider some energy integrals under slow growth, and we prove that the local minimizers are locally Lipschitz continuous. Many examples are given, either with subquadratic p, q- growth and/or anisotropic growth.

2022 - On the validity of variational inequalities for obstacle problems with non-standard growth [Articolo su rivista]
Eleuteri, M.; di Napoli, A. P.
abstract

The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality expressed in terms of a duality formula between the constrained minimizers and the corresponding dual maximizers, without any smallness assumptions on the gap between growth and coercitivity exponents. Our results rely on techniques based on Convex Analysis that consist in establishing pointwise relations that are preserved passing to the limit. We point out that we are able to deal with very general obstacle quasi-continuous up to a subset of zero capacity.

2021 - A Compactness Result for the Sobolev Embedding via Potential Theory [Capitolo/Saggio]
Camellini, Filippo; Eleuteri, Michela; Polidoro, Sergio
abstract

In this note we give a proof of the Sobolev and Morrey embedding theorems based on the representation of functions in terms of the fundamental solution of suitable partial differential operators. We also prove the compactness of the Sobolev embedding. We first describe this method in the classical setting, where the fundamental solution of the Laplace equation is used, to recover the classical Sobolev and Morrey theorems. We next consider degenerate Kolmogorov equations. In this case, the fundamental solution is invariant with respect to a non-Euclidean translation group and the usual convolution is replaced by an operation that is defined in accordance with this geometry. We recover some known embedding results and we prove the compactness of the Sobolev embedding. We finally apply our regularity results to a kinetic equation.

2021 - Flowers and AI, a laboratory experience to learn the mathematics of machine learning [Relazione in Atti di Convegno]
Monari, P.; Scaltriti, S.; Rebecchi, F.; Eleuteri, M.; Barca, D.
abstract

2021 - Il concetto di tangenza: un percorso verticale a partire dalla scuola primaria [Relazione in Atti di Convegno]
Benassi, Carlo 6/8/1962; Eleuteri, Michela; Ferri, Caterina
abstract

2021 - Regularity results for a class of obstacle problems with p, q-growth conditions [Articolo su rivista]
Caselli, M.; Eleuteri, M.; Passarelli Di Napoli, A.
abstract

In this paper we prove the the local Lipschitz continuity for solutions to a class of obstacle problems of the type(formula presented) Here K () is the set of admissible functions z 2 u0 +W1;p() for a given u0 2 W1;p() such that z a.e. in , being the obstacle and being an open bounded set of Rn, n 2. The main novelty here is that we are assuming that the integrand F(x;Dz) satises (p; q)-growth conditions and as a function of the x-variable belongs to a suitable Sobolev class. We remark that the Lipschitz continuity result is obtained under a sharp closeness condition between the growth and the ellipticity exponents. Moreover, we impose less restrictive assumptions on the obstacle with respect to the previous regularity results. Furthermore, assuming the obstacle is locally bounded, we prove the local boundedness of the solutions to a quite large class of variational inequalities whose principal part satisfies non standard growth conditions.

2021 - The fundamental theorem of integral calculus: a Volterra’s generalization applied to flat functions [Articolo su rivista]
Benassi, Carlo 6/8/1962; Eleuteri, Michela
abstract

2021 - Γ-convergence for power-law functionals with variable exponents [Articolo su rivista]
Eleuteri, M.; Prinari, F.
abstract

We study the Γ-convergence of the functionals Fn(u):=||f(⋅,u(⋅),Du(⋅))||pjavax.xml.bind.JAXBElement@1599978c(⋅) and [Formula presented] defined on X∈{L1(Ω,Rd),L∞(Ω,Rd),C(Ω,Rd)} (endowed with their usual norms) with effective domain the Sobolev space W1,pjavax.xml.bind.JAXBElement@17c9c5d8(⋅)(Ω,Rd). Here Ω⊆RN is a bounded open set, N,d≥1 and the measurable functions pn:Ω→[1,+∞) satisfy the conditions ess supΩpn≤βess infΩpn<+∞ for a fixed constant β>1 and ess infΩpn→+∞ as n→+∞. We show that when f(x,u,⋅) is level convex and lower semicontinuous and it satisfies a uniform growth condition from below, then, as n→∞, the sequence (Fn)nΓ-converges in X to the functional F represented as F(u)=||f(⋅,u(⋅),Du(⋅))||∞ on the effective domain W1,∞(Ω,Rd). Moreover we show that the Γ-limnFn is given by the functional F(u):=0if||f(⋅,u(⋅),Du(⋅))||∞≤1,+∞otherwiseinX.

2020 - Asymptotic Stability of Solutions to the Porous Media System with Hysteresis [Articolo su rivista]
Eleuteri, Michela; Krejci, Pavel
abstract

2020 - Fatigue and phase transition in an oscillating elastoplastic beam [Articolo su rivista]
Eleuteri, Michela; Gavioli, Chiara; Kopfová, Jana
abstract

2020 - Periodic solutions of a hysteresis model for breathing [Articolo su rivista]
Eleuteri, Michela; Ipocoana, Erica; Kopfova, Jana; Krejci, Pavel
abstract

2020 - Regularity for scalar integrals without structure conditions [Articolo su rivista]
Eleuteri, M.; Marcellini, P.; Mascolo, E.
abstract

Integrals of the Calculus of Variations with p, q-growth may have not smooth minimizers, not even bounded, for general p, q exponents. In this paper we consider the scalar case, which contrary to the vector-valued one allows us not to impose structure conditions on the integrand f (x, ξ) with dependence on the modulus of the gradient, i.e. f(x , ξ) = g (x,|ξ|). Without imposing structure conditions, we prove that if q p is sufficiently close to 1, then every minimizer is locally Lipschitz-continuous.

2020 - Regularity results for a class of non-differentiable obstacle problems [Articolo su rivista]
Eleuteri, M.; Passarelli di Napoli, A.
abstract

In this paper we prove the higher differentiability in the scale of Besov spaces of the solutions to a class of obstacle problems of the type min∫ΩF(x,z,Dz):z∈Kψ(Ω). Here Ω is an open bounded set of Rn, n≥2, ψ is a fixed function called obstacle and Kψ(Ω) is set of admissible functions z∈W1,p(Ω) such that z≥ψ a.e. in Ω. We assume that the gradient of the obstacle belongs to a suitable Besov space. The main novelty here is that we are not assuming any differentiability on the partial maps x↦F(x,z,Dz) and z↦F(x,z,Dz), but only their Hölder continuity.

2019 - A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients [Articolo su rivista]
Anceschi, Francesca; Eleuteri, Michela; Polidoro, Sergio
abstract

We consider weak solutions of second-order partial differential equations of Kolmogorov-Fokker-Planck-type with measurable coefficients in the form ∂tu + (v,∇xu) = div(A(v,x,t)∇vu) + (b(v,x,t),∇vu) + f, (v,x,t) ϵ2n+1, where A is a symmetric uniformly positive definite matrix with bounded measurable coefficients; f and the components of the vector b are bounded and measurable functions. We give a geometric statement of the Harnack inequality recently proved by Golse et al. As a corollary, we obtain a strong maximum principle.

2019 - Breathing as a Periodic Gas Exchange in a Deformable Porous Medium [Relazione in Atti di Convegno]
Eleuteri, M.; Ipocoana, Erica; Kopfova, J.; Krejci, P.
abstract

We propose to model the mammalian lungs as a viscoelastic deformable porous medium with a hysteretic pressure–volume relationship described by the Preisach operator. Breathing is represented as an isothermal time-periodic process with the gas exchange between the interior and exterior of the body. The main result consists of proving the existence of a periodic solution under an arbitrary periodic forcing in suitable function spaces.

2019 - Local lipschitz continuity of minimizers with mild assumptions on the x-dependence [Articolo su rivista]
Eleuteri, M.; Marcellini, P.; Mascolo, E.
abstract

We are interested in the regularity of local minimizers of energy integrals of the Calculus of Variations. Precisely, let Ω be an open subset of Rn. Let f (x, ξ) be a real function defined in Ω × Rnsatisfying the growth condition |fξx(x, ξ)| ≤ h (x) |ξ|p−1, for x ∈ Ω and ξ ∈ Rnwith |ξ| ≥ M0for some M0≥ 0, with h ∈ Lrloc(Ω) for some r > n. This growth condition is more general than those considered in the mathematical literature and allows us to handle some cases recently studied in similar contexts. We associate to f (x, ξ) the so-called natural p−growth conditions on the second derivatives fξξ(x, ξ); i.e., (p − 2) −growth for |fξξ(x, ξ)| from above and (p − 2) −growth from below for the quadratic form (fξξ(x, ξ) λ, λ); for details see either (3) or (7) below. We prove that these conditions are sufficient for the local Lipschitz continuity of any minimizer u ∈ Wloc1,p(Ω) of the energy integral fΩf (x, Du (x)) dx .

2019 - Regularity and long-time behavior for a thermodynamically consistent model for complex fluids in two space dimensions [Articolo su rivista]
Eleuteri, Michela; Gatti, Stefania; Schimperna, Giulio
abstract

We consider a thermodynamically consistent model for the evolution of thermally conducting two-phase incompressible fluids. Complementing previous results, we prove additional regularity properties of solutions in the case when the evolution takes place in the two-dimensional flat torus. Thanks to improved regularity, we can also prove uniqueness and characterize the long-time behavior of trajectories showing existence of the global attractor in a suitable phase space.

2018 - Elasto-plastic contact problems with heat exchange and fatigue [Articolo su rivista]
Eleuteri, Michela; Kopfová, Jana
abstract

We deal with a one-dimensional temperature dependent model for fatigue accumulation in a moving visco-elasto-plastic material in contact with an elasto-plastic obstacle. The problem for the unknown displacement and temperature is formulated using hysteresis operators as solution operators of the underlying variational inequalities. The existence result for this problem, consisting of the momentum and energy balance equations and an evolution equation for the fatigue, is obtained using a priori estimates established for the space discretized problem. The uniqueness result follows from the Lipschitz continuity of the nonlinearities.

2018 - Higher differentiability for solutions to a class of obstacle problems [Articolo su rivista]
Eleuteri, Michela; PASSARELLI DI NAPOLI, Antonia
abstract

We establish the higher differentiability of integer and fractional order of the solutions to a class of obstacle problems assuming that the gradient of the obstacle possesses an extra (integer or fractional) differentiability property

2018 - On a new model for fatigue and phase transition in an oscillating elastoplastic plate [Articolo su rivista]
Eleuteri, Michela; Kopfova, Jana
abstract

We consider a thermodynamic model for fatigue accumulation in an oscillating elastoplastic plate based on the two hypotheses that the fatigue accumulation rate is proportional to the plastic part of the dissipation rate and that the material can partially recover by the effect of melting. For the full model, consisting of the momentum and energy balances, an evolution equation for the fatigue rate and a differential inclusion for the phase dynamics, we prove existence of a solution in the given time interval.

2016 - 10th International Symposium on Hysteresis Modeling and Micromagnetics (HMM 2015) [Curatela]
Dimian, Mihai; Cardelli, Ermanno; Cimpoesu, Dorin; Eleuteri, Michela; Enachescu, Cristian
abstract

This issue is concerned with the proceedings of the 10th International Symposium on Hysteresis Modeling and Micromagnetics (HMM 2015)

2016 - Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids [Articolo su rivista]
Eleuteri, Michela; Rocca, Elisabetta; Schimperna, Giulio
abstract

We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. The model was recently introduced in [11] where existence of weak solutions was proved in three space dimensions. Here, we aim to study the properties of solutions in the two-dimensional case. In particular, we can show existence of global in time solutions satisfying a stronger formulation of the model with respect to the one considered in [11].

2016 - Lipschitz continuity for energy integrals with variable exponents [Articolo su rivista]
Eleuteri, Michela; Marcellini, Paolo; Mascolo, Elvira
abstract

A regularity result for integrals of the Calculus of Variations with variable exponents is presented. Precisely, we prove that any vector-valued minimizer of an energy integral over an open set WHRn, with variable exponent p(x) in the Sobolev class W1; r loc W for some r > n, is locally Lipschitz continuous in W and an a priori estimate holds.

2016 - Lipschitz estimates for systems with ellipticity conditions at infinity [Articolo su rivista]
Eleuteri, Michela; Marcellini, Paolo; Mascolo, Elvira
abstract

In the general vector-valued case N≥ 1 , we prove the Lipschitz continuity of local minimizers to some integrals of the calculus of variations of the form ∫Ωg(x,|Du|)dx, with p, q-growth conditions only for | Du| → + ∞ and without further structure conditions on the integrand g= g(x, | Du|). We apply the regularity results to weak solutions to nonlinear elliptic systems of the form ∑i=1n∂∂xiaiα(x,Du)=0, α= 1 , 2 , … , N.

2015 - A new phase field model for material fatigue in an oscillating elastoplastic beam [Articolo su rivista]
Eleuteri, Michela; Kopfová, Jana; Krejčí, Pavel
abstract

We pursue the study of fatigue accumulation in an oscillating elastoplastic beam under the additional hypothesis that the material can partially recover by the effect of melting. The full system consists of the momentum and energy balance equations, an evolution equation for the fatigue rate, and a differential inclusion for the phase dynamics. The main result consists in proving the existence and uniqueness of a strong solution.

2015 - On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids [Articolo su rivista]
Eleuteri, Michela; Rocca, Elisabetta; Schimperna, Giulio
abstract

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature on the flow are taken into account. In the mathematical model, the evolution of the velocity u is ruled by the Navier-Stokes system with temperature-dependent viscosity, while the order parameter ϕ representing the concentration of one of the components of the fluid is assumed to satisfy a convective Cahn-Hilliard equation. The effects of the temperature are prescribed by a suitable form of the heat equation. However, due to quadratic forcing terms, this equation is replaced, in the weak formulation, by an equality representing energy conservation complemented with a differential inequality describing production of entropy. The main advantage of introducing this notion of solution is that, while the thermodynamical consistency is preserved, at the same time the energy-entropy formulation is more tractable mathematically. Indeed, global-in-time existence for the initial-boundary value problem associated to the weak formulation of the model is proved by deriving suitable a priori estimates and showing weak sequential stability of families of approximating solutions

2015 - Preface: Special issue on rate-independent evolutions and hysteresis modelling [Breve Introduzione]
Bosia, Stefano; Eleuteri, Michela; Rocca, Elisabetta; Valdinoci, Enrico
abstract

The interest in hysteresis and rate-independent phenomena is shared by scientists with a great variety of dierent backgrounds. We can encounter these processes in several situations of common life: for instance in elasto-plasticity, ferromag- netism, shape-memory alloys, phase transitions. Beyond physics, hysteresis and rate-independent phenomena appear also in engineering, biology, economics as well as in many other settings, playing an important role in many applications. The com- plexity arising in these elds necessarily requires a joint contribution of experts with dierent backgrounds and skills. Therefore, only synergy and cooperation among these several people can lead to concrete advances in the technological capabilities of our society. This special issue of Discrete and Continuous Dynamical Systems is devoted to the latest advances and trends in the modelling and in the analysis of this family of complex phenomena. In particular, we gathered contributions from dierent elds of science (mathematical analysis, mathematical physics, engineering) with the intent of presenting an updated picture of current research directions, oering a new and interdisciplinary perspective in the study of these processes. Motivated by the Spring School on Rate-independent Evolutions and Hysteresis Modelling, held at the Politecnico di Milano and University of Milano on May 27-31, 2013, this special issue contains dierent kinds of original contributions: some of them originate from the courses held in that occasion and from the discussions they stimulated, but are here presented in a new perspective; some others instead are original contributions in related topics. All the papers are written in the clearest possible language, accessible also to students and non-experts of the eld, with the intent to attract and introduce them to this topic.

2015 - Special issue of Mathematica Bohemica dedicated to Equadiff13 - Volume 140 No. 2 [Curatela]
Eleuteri, Michela; Krejci, Pavel
abstract

This is the third of the 4 volumes of the journal Mathematica Bohemica dedicated to the International Conference EQUADIFF13, Praga (Czech Republic), August 26-30, 2013.

2015 - Special issue of Mathematica Bohemica dedicated to Equadiff13 - Volume 140 No. 4 [Curatela]
Eleuteri, Michela; Krejci, Pavel
abstract

This is the last of the 4 volumes of the journal Mathematica Bohemica dedicated to the International Conference EQUADIFF13, Praga (Czech Republic), August 26-30, 2013.

2014 - Fatigue accumulation in a thermo-visco-elastoplastic plate [Articolo su rivista]
Eleuteri, Michela; Kopfovà, Jana; Krejčí, Pavel
abstract

We consider a thermodynamic model for fatigue accumulation in an oscillating elastoplastic Kirchhoff plate based on the hypothesis that the fatigue accumulation rate is proportional to the plastic part of the dissipation rate. For the full model with periodic boundary conditions we prove existence of a solution in the whole time interval.

2014 - Fatigue and phase transition in an oscillating plate [Articolo su rivista]
Bosia, Stefano; Eleuteri, Michela; Kopfová, Jana; Krejčí, Pavel
abstract

We propose a temperature-dependent model for fatigue accumulation in an oscillating elasto-plastic plate accounting also for phase transition. The main modeling hypothesis is that the fatigue rate is proportional to the dissipation rate. We show thermodynamic consistency of the model and discuss a possible choice of the evolution equation for the fatigue parameter m. © 2013 Elsevier B.V.

2014 - Special Issue of Mathematica Bohemica dedicated to Equadiff13 - Volume 139 No. 2 [Curatela]
Eleuteri, Michela; Krejci, Pavel
abstract

This is the first of the 4 volumes of the journal Mathematica Bohemica dedicated to the International Conference EQUADIFF13, Praga (Czech Republic), August 26-30, 2013.

2014 - Special Issue on "Rate-independent evolutions and hysteresis modelling" [Curatela]
Bosia, Stefano; Eleuteri, Michela; Rocca, Elisabetta; Valdinoci, Enrico
abstract

The interest in hysteresis and rate-independent phenomena is shared by scientists with a great variety of different backgrounds. We can encounter these processes in several situations of common life: for instance in elasto-plasticity, ferromagnetism, shape memory alloys, phase transitions. Beyond physics, hysteresis and rate-independent phenomena appear also in engineering, biology, economics as well as in many other settings, playing an important role in many applications. The complexity arising in these fields necessarily requires a joint contribution of experts with different backgrounds and skills. Therefore, only synergy and cooperation among these several people can lead to concrete advances in the technological capabilities of our society. This special issue of Rendiconti del Seminario Matematico is devoted to the latest advances and trends in the modelling and in the analysis of this family of complex phenomena, motivated by the Spring School on Rate-independent Evolutions and Hysteresis Modelling, held at the Politecnico di Milano and University of Milano on May 27-31, 2013. In particular, we gathered contributions from different area of mathematics, with the intent of presenting an updated picture of current research directions, offering a new perspective in the study of these processes.

2014 - Special issue of Mathematica Bohemica dedicated to Equadiff13 - Volume 139 No. 4 [Curatela]
Eleuteri, Michela; Krejci, Pavel
abstract

This is the second of the 4 volumes of the journal Mathematica Bohemica dedicated to the International Conference EQUADIFF13, Praga (Czech Republic), August 26-30, 2013.

2014 - Thermal control of a rate-independent model for permanent inelastic effects in shape memory materials [Articolo su rivista]
Eleuteri, Michela; Luca, Lussardi
abstract

We address the thermal control of the quasi-static evolution of a polycrystalline shape memory alloy specimen. The thermomechanical evolution of the body is described by means of an extension of the phenomenological Souza-Auricchio model accounting also for permanent inelastic effects. By assuming to be able to control the temperature of the body in time we determine the corresponding quasi-static evolution in the energetic sense. Using results by Rindler, we prove the existence of optimal controls for a suitably large class of cost functionals.

2013 - Determination of the equivalent anisotropy properties of polycrystalline magnetic materials: Theoretical aspects and numerical analysis [Articolo su rivista]
Bottauscio, Oriano; Piat, Valeria Chiadò; Eleuteri, Michela; Lussardi, Luca; Manzin, Alessandra
abstract

The aim of this paper is the determination of the equivalent anisotropy properties of polycrystalline magnetic materials, modeled as an assembly of monocrystalline grains with a stochastic spatial distribution of easy axes. The theory of Γ-convergence is here adopted to homogenize the anisotropic contribution in the energy functional and derive the equivalent anisotropy properties. The reliability of this approach is investigated focusing on the computation of the static hysteresis loops of polycrystalline magnetic thin films, starting from the numerical integration of the Landau–Lifshitz–Gilbert equation

2013 - Fatigue accumulation in an oscillating plate [Articolo su rivista]
Eleuteri, Michela; Kopfova, Jana; Krejci, Pavel
abstract

A thermodynamic model for fatigue accumulation in an oscillating elastoplastic Kirchhoff plate based on the hypothesis that the fatigue accumulation rate is proportional to the dissipation rate, is derived for the case that both the elastic and the plastic material characteristics change with increasing fatigue. We prove the existence of a unique solution in the whole time interval before a singularity (material failure) occurs under the simplifying hypothesis that the temperature history is a priori given

2013 - Global regularity and stability of solutions to obstacle problems with nonstandard growth [Articolo su rivista]
Eleuteri, Michela; Harjulehto, Petteri; Lukkari, Teemu
abstract

We study the regularity properties of solutions to the single and double obstacle problem with non standard growth. Our main results are a global reverse Hölder inequality, Hölder continuity up to the boundary, and stability of solutions with respect to continuous perturbations in the variable growth exponent

2013 - Non-isothermal cyclic fatigue in an oscillating elastoplastic beam [Articolo su rivista]
Eleuteri, Michela; Kopfová, Jana; Krejčí, Pavel
abstract

We propose a temperature dependent model for fatigue accumulation in an oscillating elastoplastic beam. The full system consists of the momentum and energy balance equations, and an evolution equation for the fatigue rate. The main modeling hypothesis is that the fatigue accumulation rate is proportional to the dissipation rate. In nontrivial cases, the process develops a thermal singularity in finite time. The main result consists in proving the existence and uniqueness of a strong solution in a time interval depending on the size of the data.

2013 - Thermal control of the souza-auricchio model for shape memory alloys [Articolo su rivista]
Eleuteri, Michela; Lussardi, Luca; Stefanelli, Ulisse
abstract

We address the thermal control of the quasi-static evolution of a polycrystalline shape memory alloy specimen. The thermomechanical evolution of the body is described by means of the phenomenological SouzaAuricchio model. By assuming to be able to control the temperature of the body in time we determine the corresponding quasi-static evolution in the energetic sense. By recovering in this context a result by Rindler, we prove the existence of optimal controls for a suitably large class of cost functionals and comment on their possible approximation.

2012 - A thermodynamic model for material fatigue under cyclic loading [Articolo su rivista]
Eleuteri, Michela; Kopfová, Jana; Krejčí, Pavel
abstract

We propose a temperature dependent model for fatigue accumulation in an oscillating elastoplastic plate. The full system consists of the momentum and energy balance equations, and an evolution equation for the fatigue rate. The main modeling hypothesis is that the fatigue rate is proportional to the dissipation rate. In nontrivial cases, the process develops a singularity (material failure) in finite time. © 2011 Elsevier B.V. All rights reserved.

2012 - Homogenization of random anisotropy properties in polycrystalline magnetic materials [Articolo su rivista]
Bottauscio, Oriano; Chiadò Piat, Valeria; Eleuteri, Michela; Lussardi, Luca; Manzin, Alessandra
abstract

This paper is devoted to the determination of the equivalent anisotropy properties of polycrystalline magnetic materials, modelled by an assembly of monocrystalline grains with a stochastic spatial distribution of easy axes. The mathematical theory of Γ-convergence is applied to homogenize the anisotropic term in the Gibbs free energy. The procedure is validated focusing on the micromagnetic computation of reversal processes in polycrystalline magnetic thin films. © 2011 Elsevier B.V. All rights reserved.

2011 - A Hölder continuity result for a class of obstacle problems under non standard growth conditions [Articolo su rivista]
Eleuteri, Michela; Habermann, Jens
abstract

We prove Hölder continuity results for a class of obstacle problems under nonstandard growth conditions. We do not assume any quantitative continuity of the integrand function f.

2011 - A rate-independent model for permanent inelastic effects in shape memory materials [Articolo su rivista]
Eleuteri, Michela; Lussardi, Luca; Stefanelli, Ulisse
abstract

This paper addresses a three-dimensional model for isothermal stress-induced transformation in shape memory polycrystalline materials in presence of permanent inelastic effects. The basic features of the model are recalled and the constitutive and the three-dimensional quasi-static evolution problem are proved to be well-posed. Finally, we discuss the convergence of the model to reduced/former ones by means of a rigorous Γ-convergence analysis.

2011 - Global regularity and stability of solutions to elliptic equations with nonstandard growth [Articolo su rivista]
Eleuteri, Michela; Harjulehto, Petteri; Lukkari, Teemu
abstract

We study the regularity properties of solutions to elliptic equations similar to the p(·)-Laplacian. Our main results are a global reverse H¨older inequality, H¨older continuity up to the boundary, and stability of solutions with respect to continuous perturbations in the variable growth exponent. We assume that the complement of the domain is uniformly fat in a capacitary sense. As technical tools, we derive a capacitary Sobolev–Poincar´e inequality, and a version of Hardy’s inequality

2010 - Calderón-Zygmund type estimates for a class of obstacle problems with p(x) growth [Articolo su rivista]
Eleuteri, Michela; Habermann, Jens
abstract

For local minimizers of general quasiconvex integral functionals with p(x) growth in the class of obstacle problems, we show estimates of Calderón–Zygmund type provided that the exponent function p satisfies a suitable continuity condition.

2010 - On a Neumann parabolic problem with hysteresis: the 3D case [Relazione in Atti di Convegno]
Eleuteri, Michela; Pavel, Krejci
abstract

A parabolic equation in three space variables with a Preisach hysteresis operator and with homogeneous Neumann boundary conditions is shown to admit a unique global regular solution; this can be used to prove the asymptotic stabilization of the solution. The results of this paper improve the content of Ref. [5], where the regularity of the solution was obtained under appropriate smallness conditions on the initial data.

2010 - Stability of solutions of the double obstacle problem on metric spaces [Relazione in Atti di Convegno]
Eleuteri, Michela; Farnana, Z; Kansanen, O. E; Korte, R.
abstract

We study the regularity properties of solutions to the double obstacle problem in a metric space. Our main results are a global reverse Hoelder inequality, and stability of solutions. We assume the space supports a weak Poincaré inequality and a doubling measure. Furthermore we assume that the complement of the domain is uniformly thick in a capacitary sense

2010 - Uniqueness and decay estimates for a class of parabolic partial differential equations with hysteresis and convection [Articolo su rivista]
Eleuteri, Michela; Kopfová, Jana
abstract

We deal in detail with the question of existence, uniqueness and asymptotic behaviour of solutions to a parabolic equation with hysteresis and convection. This equation is part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates.The result of this paper complements the content of a previous paper of the first author, where existence of the solution has been proved under fairly general assumptions on the hysteresis operator and the uniqueness was only obtained for a restricted class of hysteresis operators.

2009 - Long time behaviour for a PDE with hysteresis arising in electromagnetism [Articolo su rivista]
Eleuteri, Michela
abstract

In some recent papers, the concept of outward pointing property has been used as a tool within the mathematical investigation of equations involving hysteresisoperatorsandhasbeenconsideredforthestopoperator, theplayoperator, Prandtl-Ishlinski˘ı operators, Preisach and inverse Preisach operators. In this paper we show, as an application of this theory, a stability result for solutions of a PDE containing the inverse of a Preisach hysteresis operator and appearing in the context of electromagnetic processes.

2009 - Magnetohydrodynamic flow with hysteresis [Articolo su rivista]
Eleuteri, Michela; Jana, Kopfova; Krejčí, Pavel
abstract

We consider a model system describing the two-dimensional flow of a conducting fluid surrounded by a ferromagnetic solid under the influence of the hysteretic response of the surrounding medium. We assume that this influence can be represented by the Preisach hysteresis operator. Existence and uniqueness of solutions for the resulting system of PDEs with hysteresis nonlinearities is established in the convexity domain of the Preisach operator.

2008 - On a model for electromagnetic processes inside and outside a ferromagnetic body [Articolo su rivista]
Brokate, Martin; Eleuteri, Michela; Krejčí, Pavel
abstract

One-dimensional Maxwell’s equations are considered in a ferromagnetic body surrounded by vacuum. Existence and uniqueness of solution for the resulting system of P.D.E.s with hysteresis on the whole real line is proved under suitable constitutive hypotheses

2008 - On a model with hysteresis arising in magnetohydrodynamics [Articolo su rivista]
Eleuteri, Michela; Kopfová, Jana; Krejčí, Pavel
abstract

We study the flow of a conducting fluid surrounded by a ferromagnetic solid, under the influence of the hysteretic response of the surrounding medium. We assume that this influence can be represented by the Preisach model and show existence of a solution of the resulting nonlinear system of PDEs in the convexity domain of the Preisach operator. © 2007 Elsevier B.V. All rights reserved.

2008 - On a parabolic equation with hysteresis and convection: A uniqueness result [Articolo su rivista]
Eleuteri, Michela; Kopfová, J.
abstract

A uniqueness result for a parabolic partial differential equation with hysteresis and convection is established. This equation is a part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates. The result of this paper complements the content of [6], where existence of the solution has been proved under fairly general assumptions on the hysteresis operator and the uniqueness was obtained only for a restricted class of hysteresis operators © 2008 IOP Publishing Ltd.

2008 - Outward pointing inverse Preisach operators [Articolo su rivista]
Eleuteri, Michela; Klein, Olaf; Krejčí, Pavel
abstract

In some recent papers, the concept of outward pointing operators has been used as a tool within the mathematical investigation of equations involving hysteresis operators and has been considered for the stop operator, the play operator, Prandtl-Ishlinskiidotlesš operators and Preisach operators. Now, for inverse Preisach operators conditions will be discussed which ensure that the outward pointing property is satisfied. As an application of the theory, a stability result for solutions of a P.D.E. with hysteresis appearing in the context of electromagnetic processes is derived. © 2007 Elsevier B.V. All rights reserved.

2008 - Regularity results for a class of obstacle problems under nonstandard growth conditions [Articolo su rivista]
Eleuteri, Michela; Habermann, Jens
abstract

We prove regularity results for minimizers of some general integral functionals in the class K :={u∈W^{1,p(x)}(Ω,R): u > ψ}, where ψ :Ω →R is a fixed function and f is quasi-convex and fulfills a p(x)-growth condition with growth exponent p:Ω →(1,∞).

2008 - Wellposedness results for a class of parabolic partial differential equations with hysteresis [Articolo su rivista]
Eleuteri, Michela
abstract

In this paper we deal with the mathematical investigation of a class of parabolic partial differential equations containing a continuous hysteresis operator arising in the context of magnetohydrodynamics. The main result we achieve is the existence of a weak solution by means of a technique based on an implicit time discretization scheme. Uniqueness is obtained under some suitable monotonicity assumptions on the hysteresis operator; finally we also analyse the dependence of the solution on the data.

2007 - Alcune equazioni alle derivate parziali con isteresi [Articolo su rivista]
Eleuteri, Michela
abstract

In questo lavoro si presentano alcuni risultati ottenuti nella tesi di dottorato. Lo scopo della mia tesi di dottorato è stato quello di dimostrare alcuni risultati riguardanti certe nuove classi di equazioni alle derivate parziali contenenti un operatore di isteresi continuo. Ho cercato di focalizzare la mia attenzione sulla buona positura dei miei modelli, lavorando, quando possibile, con differenti tipi di condizioni al bordo. Sono inoltre riuscita a stabilire anche un risultato di comportamento asintotico per una classe di E.D.P. di tipo parabolico.

2007 - An asymptotic convergence result for a system of partial differential equations with hysteresis [Articolo su rivista]
Eleuteri, Michela; Krejčí, Pavel
abstract

A partial differential equation motivated by electromagnetic field equations in ferromagnetic media is considered with a relaxed rate dependent constitutive relation. It is shown that the solutions converge to the unique solution of the limit parabolic problem with a rate independent Preisach hysteresis constitutive operator as the relaxation parameter tends to zero.

2007 - An existence result for A P.D.E. with hysteresis, convection and a nonlinear boundary condition [Articolo su rivista]
Eleuteri, Michela
abstract

In this paper a partial differential equation containing a continuous hysteresis operator and a convective term is considered. This model equation, which appears in the context of magnetohydrodynamics, is coupled with a nonlinear boundary condition containing a memory operator. Under suitable assumptions, an existence result is achieved using an implicit time discretization scheme.

2007 - Asymptotic behavior of a Neumann parabolic problem with hysteresis [Articolo su rivista]
Eleuteri, Michela; Krejčí, Pavel
abstract

A parabolic equation in two or three space variables with a Preisach hysteresis operator and with homogeneous Neumann boundary conditions is shown to admit a unique global regular solution. A detailed investigation of the Preisach memory dynamics shows that the system converges to an equilibrium in the state space of all admissible Preisach memory configurations as time tends to infinity

2007 - Regularity results for a class of obstacle problems [Articolo su rivista]
Eleuteri, Michela
abstract

We prove some optimal regularity results for minimizers of some general integral functionals belonging to the class K := {u ∈ W^{1,p}(Ω): u > ψ}, where ψ is a fixed function, under standard growth conditions of p-type

2007 - Some P.D.E.s with hysteresis [Relazione in Atti di Convegno]
Eleuteri, Michela
abstract

We present some results concerning two classes of P.D.E.s containing a continuous hysteresis operator. We introduce a weak formulation in Sobolev spaces for a Cauchy problem; under suitable assumptions on the hysteresis operator, we state some existence results. The presentation of the paper is quite general, as we avoid to describe all the details of the proof of the theorems involved

2007 - Well-posedness results for a class of partial differential equations with hysteresis arising in electromagnetism [Articolo su rivista]
Eleuteri, Michela
abstract

We consider an evolutionary PDE motivated by models for electromagnetic processes in ferromagnetic materials. Magnetic hysteresis is represented by means of a hysteresis operator. Under suitable assumptions, an existence and uniqueness theorem is obtained, together with the Lipschitz continuous dependence on the data and some further regularity results. The discussion of the behaviour of the solution in dependence on physical parameters of the problem is also outlined.

2004 - Hölder continuity results for a class of functionals with non standard growth [Articolo su rivista]
Eleuteri, Michela
abstract

In questo lavoro si provano risultati di regolarità per minimi di funzionali scalari a crescita non-standard di tipo p(x). Si considerano per la funzione esponente p(x) > 1 ipotesi di regolarità ottimali.