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Stefania PERROTTA

Ricercatore Universitario presso: Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Matematica


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Pubblicazioni

2019 - Exact controllability of infinite dimensional systems with controls of minimal norm [Articolo su rivista]
Malaguti, Luisa; Perrotta, Stefania; Taddei, Valentina
abstract

The paper deals with the exact controllability of a semilinear system in a separable Hilbert space. A bounded linear part is considered and a linear control introduced. The state space is compactly embedded in a Banach space and the nonlinear term is continuous in its state variable in the norm of the Banach space. An infinite sequence of finite dimen- sional controllability problems is introduced and the solution is obtained by a limiting procedure. To the best of our knowledge, the method is new in controllability theory. An application to an integro-differential system in euclidean spaces completes the discussion.


2013 - Polyconvex energies and cavitation [Articolo su rivista]
P., Celada; Perrotta, Stefania
abstract

We study the existence of singular minimizers in the class of radial deformations for polyconvex energies that grow linearly with respect to the Jacobian.


2008 - A correction of the paper "On minima of radially symmetric functionals of the gradient" [Articolo su rivista]
A., Cellina; Perrotta, Stefania
abstract

We prove a theorem for the existence of solutions to a variational problem, under assumptions that do not require the convexity of the integrand.


2007 - On a class of nonconvex Bolza problems related to Blatz-Ko elastic materials. [Articolo su rivista]
P., Celada; Perrotta, Stefania
abstract

We study the existence of solutions to Bolza problems for a special class of one-dimensional, nonconvex integrals. These integrals describe the possibly singular, radial deformations of certain rubberlike materials called Blatz–Ko materials.


2002 - Existence of minimizers for nonconvex, noncoercive simple integrals. [Articolo su rivista]
P., Celada; Perrotta, Stefania
abstract

We consider the problem of minimizing autonomous, simple integrals such as \min\,\left\{ \int_0^T f\left(x(t)\,,x^\prime(t)\right)\,dt\colon\,\, \text{$x\in AC{([0\,,T])}$, $x(0)=x_0$, $x(T)=x_T$} \right\}, \tag{$\cal{P}$} where $f:{\mathbb R}\times{\mathbb R} \to [0,\infty]$ is a possibly nonconvex function with either superlinear or slow growth at infinity. Assuming that the relaxed problem ($\cal{P}^{\ast\ast}$)---obtained from ($\cal{P}$) by replacing f with its convex envelope f** with respect to the derivative variable $x^\prime$---admits a solution, we prove attainment for ($\cal{P}$) under mild regularity and growth assumptions on f and f**. We discuss various instances of growth conditions on f that yield solutions to the corresponding relaxed problem ($\cal{P}^{\ast\ast}$), and we present examples that show that the hypotheses on f and f** considered here for attainment are essentially sharp.


2001 - Minimizing nonconvex, simple integrals of product type [Articolo su rivista]
P., Celada; Perrotta, Stefania
abstract

We consider the problem of minimizing simple integrals of product type, i.e. min {integral (T)(0) g(x(t))f(x ´ (t)) dt: x is an element of AC([0, T]), x(0) = x(0), x(T) = x(T)}. where f:R --> [0, proportional to] is a possibly nonconvex, lower semicontinuous function with either superlinear or slow growth at infinity. Assuming that the relaxed problem (P**) obtained from (P) by replacing f with its convex envelope f** admits a solution. we prove attainment for (P) for every continuous, positively bounded below the coefficient g such that (i) every point t is an element ofR is squeezed between two intervals where g is monotone and (ii) g has no strict local minima. This shows in particular that, for those f such that the relaxed problem (P**) has a solution, the class of coefficients g that yield existence to (P) is dense in the space of continuous, positive Functions on R. We discuss various instances of growth conditions on f that yield solutions to (P**) and we present examples that show that the hypotheses on g considered above for attainment are essentially sharp.


2001 - On the minimum problem for nonconvex, multiple integrals of product type [Articolo su rivista]
P., Celada; Perrotta, Stefania
abstract

We consider the problem of minimizing multiple integrals of product type, i.e. (P) min [GRAPHICS] where Omega is a bounded, open set in R-N, f: R-N --> [0, infinity) is a possibly nonconvex, lower semicontinuous function with p-growth at infinity for some 1 < p < infinity and the boundary datum u(0) is in W-1,W-p(Omega) boolean AND L-infinity(Omega) (or simply in W-1,W-p(Omega) if N < p < infinity). Assuming that the convex envelope f** of f is affine on each connected component of the set {f** < f}, we prove attainment for (P) for every continuous, positively bounded below function g such that (i) every point t <is an element of> R is squeezed between two intervals where g is monotone and (ii) g has no strict local minima. This shows in particular that the class of coefficents g that yield existence to (P) is dense in the space of continuous, positive functions on R. We present examples which show that these conditions for attainment are essentially sharp.


2000 - Minimizing non-convex multiple integrals: a density result. [Articolo su rivista]
P., Celada; Perrotta, Stefania
abstract

We consider variational problems whose lagrangian is of the form f(Du)+g(u) where f is a possibly non-convex lower semicontinuous function with p-growth at infinity for some 1 < p < ∞, and the boundary datum is any function in W 1,p (Ω). Assuming that the convex envelope of f is affine on each connected component of the set {f ^∗∗ < f }, we prove the existence of solutions to (P) for every continuous function g such that (i) g has no strict local minima and (ii) every convergent sequence of extremum points of g eventually belongs to an interval where g is constant, thus showing that the set of continuous functions g that yield existence to (P) is dense in the space of continuous functions on R.


2000 - Vectorial Hamilton-Jacobi equations with rank one affine dependence on the gradient. [Articolo su rivista]
P., Celada; Perrotta, Stefania
abstract

This paper deals with Dirichlet problems for vectorial, stationary Hamilton-Jacobi equations


1999 - Nonconvex variational problems related to a hyperbolic equation [Articolo su rivista]
F., FLORES BAZAN; Perrotta, Stefania
abstract

We first prove a new Lyapunov-type theorem which will yield existence of solutions to nonconvex minimum problems involving some hyperbolic equations on rectangular domains with Darboux boundary conditions. Some problems with obstacle and bang-bang results are also considered.


1998 - Existence of solutions for a class of non convex minimum problems [Articolo su rivista]
P., Celada; Perrotta, Stefania; G., Treu
abstract

In this paper we give sufficient conditions for the existence of solutions to the problem of minimizing the integral of [f ( ∇v) + v] on a convex n-dimensional set Ω . Here f is nonnegative, nonconvex, Borel-measurable, and vanishes on the boundary of a convex n-dimensional set K.


1998 - Functions with prescribed singular values of the gradient. [Articolo su rivista]
P., Celada; Perrotta, Stefania
abstract

We prove the existence of infinitely many vector-valued Lipschitz-continuous functions u on an open set Ω satisfying suitable Dirichlet boundary conditions such that the singular values of the gradient matrix ∇u, agree a.e. on Ω with N given positive, bounded and lower semicontinuous functions.


1998 - On the validity of the maximum principle and of the Euler-Lagrange equation for a minimum problem depending on the gradient [Articolo su rivista]
A., Cellina; Perrotta, Stefania
abstract

We consider the limiting case alpha = infinity of the problem of minimizing integral(Omega) (\\del u(x)\\(alpha) + g(u))dx on u is an element of + u(0) + W-0(1, alpha) (Omega); where g is differentiable and strictly monotone. If this infimum is finite, it is evidently attained; we show that any minimizing function u satisfies the appropriate form of the Euler-Lagrange equation, i.e., for some function p, div p(x) = g'(u(x)) for p(x) is an element of partial derivative(jB)(del(x)); where j(B) is the indicator function of the closed unit ball in the Euclidean norm of R-N and partial derivative is the subdifferential of the convex function j(B).


1995 - On a problem of potential wells. [Articolo su rivista]
A., Cellina; Perrotta, Stefania
abstract

We find an explicit solution for a potential wells problem in dimension 3.


1994 - On minima of radially symmetric functionals of the gradient. [Articolo su rivista]
A., Cellina; Perrotta, Stefania
abstract

In this paper we consider the problems of the existence, the uniqueness and the qualitative properties (symmetry) of the minima to a minimization problem in the calculus of variations.


1994 - On the closure of reachable sets for control systems. [Articolo su rivista]
Perrotta, Stefania
abstract

We prove a density result related to control systems with closed reachable set.