arXiv subjects

Fernando Farroni

Publications and source records attributed to Fernando Farroni.

5 recordsLinked to original sources

arXiv2026

Well-posedness results for superlinear Fokker-Planck equations

In this manuscript we deal with a class of nonlinear Fokker-Planck equations with the following structure \[ \partial_t u - \div\big(M\nabla u+ E h(u)\big)=0, \] with $M$ a bounded elliptic matrix, $E$ a vector field in a suitable Lebesgue space, and $h(u)$ featuring a superlinear growth for $u$ large. We provide existence results of $C([0,T),L^1)$ distributional solutions to initial-boundary value problems related to the equation above together with some qualitative properties of solutions.

math.AP↗

arXiv2021

On some non-local approximation of nonisotropic Griffith-type functionals

The approximation in the sense of $Γ$-convergence of nonisotropic Griffith-type functionals, with $p-$growth ($p>1$) in the symmetrized gradient, by means of a suitable sequence of non-local convolution type functionals defined on Sobolev spaces, is analysed.

math.AP↗

arXiv2020

Nonlinear evolution problems with singular coefficients in the lower order terms

We consider a Cauchy Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the solution in the case of the infinite time horizon.

math.AP↗

arXiv2020

Noncoercive quasilinear elliptic operators with singular lower order terms

We consider a family of quasilinear second order elliptic differential operators which are not coercive and are defined by functions in Marcinkiewicz spaces. We prove the existence of a solution to the corresponding Dirichlet problem. The associated obstacle problem is also solved. Finally, we show higher integrability of a solution to the Dirichlet problem when the datum is more regular.

math.AP↗

arXiv2013

Estimates for $p$-Laplace type equation in a limit case

We study some Dirichlet problem for a $p$--Laplacian type operator in the setting of Orlicz--Zygmund space $L^q\log^{-α}L(Ω,\mathbb R^N)$, $q >1$ and $α>0$. More precisely, our aim is to establish which assuptions on the parameter $α>0$ lead to existence, uniqueness of the solution and continuity of the associated nonlinear operator.

math.AP↗