37 citations · 166 across the 12 of their papers we have counts for
13 papers
Higher order boundary Harnack principles in Dini type domains
Seongmin Jeon, Stefano Vita
Aim of this paper is to provide higher order boundary Harnack principles [De Silva-Savin 15] for elliptic equations in divergence form under Dini type regularity assumptions on bou…
Higher order boundary Harnack principle via degenerate equations
Susanna Terracini, Giorgio Tortone, Stefano Vita
As a first result we prove higher order Schauder estimates for solutions to singular/degenerate elliptic equations of type: \[ -\mathrm{div}\left(ρ^aA\nabla w\right)=ρ^af+\mathrm{d…
Boundary regularity estimates in Hölder spaces with variable exponent
Stefano Vita
We present a general blow-up technique to obtain local regularity estimates for solutions, and their derivatives, of second order elliptic equations in divergence form in Hölder sp…
A numerical study of an Heaviside function driven degenerate diffusion equation
Carlo Alberini, Raffaela Capitanelli, Stefano Finzi Vita
We analyze a nonlinear degenerate parabolic problem whose diffusion coefficient is the Heaviside function of the distance of the solution itself from a given target function. We sh…
On the time fractional heat equation with obstacle
Carlo Alberini, Raffaela Capitanelli, Mirko D'Ovidio +1
We study a Caputo time fractional degenerate diffusion equation which we prove to be equivalent to the fractional parabolic obstacle problem, showing that its solution evolves for…
Liouville type theorems and regularity of solutions to degenerate or singular problems part II: odd solutions
Yannick Sire, Susanna Terracini, Stefano Vita
We consider a class of equations in divergence form with a singular/degenerate weight Under suit…
Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions
Yannick Sire, Susanna Terracini, Stefano Vita
We consider a class of equations in divergence form with a singular/degenerate weight $$-\mathrm{div}(|y|^a A(x,y)\nabla u)=|y|^a f(x,y)\; \quad\textrm{or} \ \textrm{div}(|y|^aF(x,…
A quantitative stability estimate for the fractional Faber-Krahn inequality
Lorenzo Brasco, Eleonora Cinti, Stefano Vita
We prove a quantitative version of the Faber-Krahn inequality for the first eigenvalue of the fractional Dirichlet-Laplacian of order s. This is done by using the so-called Caffare…
On s-harmonic functions on cones
Susanna Terracini, Giorgio Tortone, Stefano Vita
We deal with non negative functions satisfying \[ \left\{ \begin{array}{ll} (-Δ)^s u_s=0 & \mathrm{in}\quad C, u_s=0 & \mathrm{in}\quad \mathbb{R}^n\setminus C, \end{array}\right.…
On the Asymptotic Growth of Positive Solutions to a Nonlocal Elliptic Blow-up System Involving Strong Competition
Susanna Terracini, Stefano Vita
For a competition-diffusion blow-up system involving the fractional Laplacian of the form \begin{equation*}\label{syst1} -(-Δ)^su=uv^2,\quad-(-Δ)^sv=vu^2,\quad u,v>0 \ \mathrm{in}…
A numerical study of a two-layer model for the growth of granular matter in a silo
Stefano Finzi Vita
The problem of filling a silo of given bounded cross-section with granular matter can be described by the two-layer model of Hadeler and Kuttler [8]. In this paper we discuss how s…
A semi-Lagrangian scheme for the game -Laplacian via -averaging
M. Falcone, S. Finzi Vita, T. Giorgi +1
We present and analyze an approximation scheme for the two-dimensional game -Laplacian in the framework of viscosity solutions. The approximation is based on a semi-Lagrangian s…
An existence result for the sandpile problem on flat tables with walls
G. Crasta, S. Finzi Vita
We derive an existence result for solutions of a differential system which characterizes the equilibria of a particular model in granular matter theory, the so-called partially ope…