
Federica SANI
Professore Associato Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede exMatematica

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Pubblicazioni
2023
 Attainability of Second Order Adams Inequalities with Navier Boundary Conditions
[Articolo su rivista]
Sani, F.
abstract
2023
 On weighted second order Adams inequalities with Navier boundary conditions
[Capitolo/Saggio]
Sani, Federica
abstract
2021
 Asymptotics for a parabolic equation with critical exponential nonlinearity
[Articolo su rivista]
Ishiwata, M.; Ruf, B.; Sani, F.; Terraneo, E.
abstract
We consider the Cauchy problem: {∂tu=Δuu+λf(u)in(0,T)×R2,u(0,x)=u0(x)inR2,where λ> 0 , f(u):=2α0ueα0u2,for someα0>0,with initial data u∈ H1(R2). The nonlinear term f has a critical growth at infinity in the energy space H1(R2) in view of the TrudingerMoser embedding. Our goal is to investigate from the initial data u∈ H1(R2) whether the solution blows up in finite time or the solution is global in time. For 0<12α0, we prove that for initial data with energies below or equal to the ground state level, the dichotomy between finite time blowup and global existence can be determined by means of a potential well argument.
2020
 A Potential Well Argument for a Semilinear Parabolic Equation with Exponential Nonlinearity
[Capitolo/Saggio]
Ishiwata, Michinori; Ruf, Bernhard; Sani, Federica; Terraneo, Elide
abstract
2020
 Sharp threshold nonlinearity for maximizing the TrudingerMoser inequalities
[Articolo su rivista]
Ibrahim, S; . Masmoudi, N.; Nakanishi, K.; Sani, F.
abstract
2019
 Spike solutions for nonlinear Schrödinger equations in 2D with vanishing potentials
[Articolo su rivista]
do O, J. M.; Gloss, E.; Sani, F.
abstract
We consider εperturbed nonlinear Schrödinger equations of the form ε2Δu+V(x)u=Q(x)f(u)inR2,where V and Q behave like (1 +  x) α with α∈ (0 , 2) and (1 +  x) β with β∈ (α, + ∞) , respectively. When f has subcritical exponential growth—by means of a weighted Trudinger–Mosertype inequality and the mountain pass theorem in weighted Sobolev spaces—we prove the existence of nontrivial mountain pass solutions, for any ε> 0 , and in the semiclassical limit, these solutions concentrate at a global minimum point of A= V/ Q. Our existence result holds also when f has critical growth, for any ε> 0.
2018
 Higher order Adams' inequality with the exact growth condition
[Articolo su rivista]
Masmoudi, Nader; Sani, Federica
abstract
Adams' inequality is the complete generalization of the TrudingerMoser inequality to the case of Sobolev spaces involving higher order derivatives. The failure of the original form of the sharp inequality when the problem is considered on the whole space Rn served as a motivation to investigate in the direction of a refined sharp inequality, the socalled Adams' inequality with the exact growth condition. Due to the difficulties arising in the higher order case from the lack of direct symmetrization techniques, this refined result is known to hold on first and secondorder Sobolev spaces only. We extend the validity of Adams' inequality with the exact growth to higher order Sobolev spaces.
2018
 Vanishingconcentrationcompactness alternative for the TrudingerMoser inequality in $Bbb R^N$
[Articolo su rivista]
Do O, Joao Marcos; Sani, Federica; Tarsi, Cristina
abstract
2017
 Elliptic equations in dimension 2 with double exponential nonlinearities
[Articolo su rivista]
Calanchi, Marta; Ruf, Bernhard; Sani, Federica
abstract
A boundary value problem on the unit disk in R2 is considered, involving an elliptic operator with a singular weight of logarithmic type and nonlinearities which are subcritical or critical with respect to the associated gradient norm. The existence of nontrivial solutions is proved, relying on variational methods. In the critical case, the associated energy functional is noncompact. A suitable asymptotic condition allows to avoid the noncompactness levels of the functional.
2017
 Stationary nonlinear Schr"odinger equations in $BbbR^2$ with potentials vanishing at infinity
[Articolo su rivista]
do O, Joao Marcos; Sani, Federica; Zhang, Jianjun
abstract
We deal with a class of 2D stationary nonlinear Schrödinger equations (NLS) involving potentials V and weights Q decaying to zero at infinity as (1 +  x α)  1, α∈ (0 , 2) , and (1 +  x β)  1, β∈ (2 , + ∞) , respectively, and nonlinearities with exponential growth of the form exp γ0s2 for some γ0> 0. Working in weighted Sobolev spaces, we prove the existence of a bound state solution, i.e. a solution belonging to H1(R2). Our approach is based on a weighted Trudinger–Mosertype inequality and the classical mountain pass theorem.
2015
 TrudingerMoser inequalities with the exact growth condition in $BbbR^N$ and applications
[Articolo su rivista]
Masmoudi, Nader; Sani, Federica
abstract
In a recent paper [19], the authors obtained a sharp version of the TrudingerMoser inequality in the whole space ℝ2, giving necessary and sufficient conditions for the boundedness and the compactness of general nonlinear functionals in W 1, 2(ℝ2). We complete this study showing that an analogue of the result in [19] holds in arbitrary dimensions N ≥2. We also provide an application to the study of the existence of ground state solutions for quasilinear elliptic equations in ℝN.
2014
 Adams' inequality with the exact growth condition in R4
[Articolo su rivista]
Masmoudi, Nader; Sani, Federica
abstract
2014
 Equivalent Moser type inequalities in R2 and the zero mass case
[Articolo su rivista]
Cassani, D.; Sani, F.; Tarsi, C.
abstract
2013
 A biharmonic equation in R4 involving nonlinearities with critical exponential growth
[Articolo su rivista]
Sani, Federica
abstract
2013
 Ground states for elliptic equations in $Bbb R^2$ with exponential critical growth
[Capitolo/Saggio]
Ruf, Bernhard; Sani, Federica
abstract
2013
 Sharp Adamstype inequalities in $BbbR^n$
[Articolo su rivista]
Ruf, Bernhard; Sani, Federica
abstract
2011
 A biharmonic equation in $scr R^4$ involving nonlinearities with subcritical exponential growth
[Articolo su rivista]
Sani, Federica
abstract
2010
 Detectability of critical points of smooth functionals from theirfinitedimensional approximations
[Articolo su rivista]
Sani, F.; Villarini, Massimo
abstract
Given a critical point of a C2functional on a separable Hilbert space, we obtain sufficient conditions for it to be detectable (i.e. `visible') from finitedimensional RayleighRitzGalerkin (RRG) approximations. While examples show that even nondegenerate critical points are, without any further restriction, not visible, we single out relevant classes of smooth functionals, e.g. the Hamiltonian action on the loop space or the functionals associated with boundary value problems for some semilinear elliptic equations, such that their nondegenerate critical points are visible from their RRG approximations.