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Federica SANI

Ricercatore t.d. art. 24 c. 3 lett. B presso: Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Matematica


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Pubblicazioni

2020 - A Potential Well Argument for a Semilinear Parabolic Equation with Exponential Nonlinearity [Capitolo/Saggio]
Ishiwata, Michinori; Ruf, Bernhard; Sani, Federica; Terraneo, Elide
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2020 - Asymptotics for a parabolic equation with critical exponential nonlinearity [Articolo su rivista]
Ishiwata, M.; Ruf, B.; Sani, F.; Terraneo, E.
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We consider the Cauchy problem: {∂tu=Δu-u+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 Trudinger-Moser 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 blow-up and global existence can be determined by means of a potential well argument.


2020 - Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities [Articolo su rivista]
Ibrahim, S; . Masmoudi, N.; Nakanishi, K.; Sani, F.
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2019 - Spike solutions for nonlinear Schrödinger equations in 2D with vanishing potentials [Articolo su rivista]
do O, J. M.; Gloss, E.; Sani, F.
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We consider ε-perturbed 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–Moser-type 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 semi-classical 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
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Adams' inequality is the complete generalization of the Trudinger-Moser 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 so-called 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 second-order Sobolev spaces only. We extend the validity of Adams' inequality with the exact growth to higher order Sobolev spaces.


2018 - Vanishing-concentration-compactness alternative for the Trudinger-Moser inequality in $Bbb R^N$ [Articolo su rivista]
Do O, Joao Marcos; Sani, Federica; Tarsi, Cristina
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2017 - Elliptic equations in dimension 2 with double exponential nonlinearities [Articolo su rivista]
Calanchi, Marta; Ruf, Bernhard; Sani, Federica
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A boundary value problem on the unit disk in R-2 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 non-trivial solutions is proved, relying on variational methods. In the critical case, the associated energy functional is non-compact. A suitable asymptotic condition allows to avoid the non-compactness 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
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We deal with a class of 2-D 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–Moser-type inequality and the classical mountain pass theorem.


2015 - Trudinger-Moser inequalities with the exact growth condition in $BbbR^N$ and applications [Articolo su rivista]
Masmoudi, Nader; Sani, Federica
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In a recent paper [19], the authors obtained a sharp version of the Trudinger-Moser 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
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2014 - Equivalent Moser type inequalities in R2 and the zero mass case [Articolo su rivista]
Cassani, D.; Sani, F.; Tarsi, C.
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2013 - A biharmonic equation in R4 involving nonlinearities with critical exponential growth [Articolo su rivista]
Sani, Federica
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2013 - Ground states for elliptic equations in $Bbb R^2$ with exponential critical growth [Capitolo/Saggio]
Ruf, Bernhard; Sani, Federica
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2013 - Sharp Adams-type inequalities in $BbbR^n$ [Articolo su rivista]
Ruf, Bernhard; Sani, Federica
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2011 - A biharmonic equation in $scr R^4$ involving nonlinearities with subcritical exponential growth [Articolo su rivista]
Sani, Federica
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2010 - Detectability of critical points of smooth functionals from theirfinite-dimensional approximations [Articolo su rivista]
Sani, F.; Villarini, Massimo
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Given a critical point of a C2-functional on a separable Hilbert space, we obtain sufficient conditions for it to be detectable (i.e. `visible') from finite-dimensional Rayleigh-Ritz-Galerkin (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.