Comparison results for solutions to p-Laplace equations with Robin boundary conditions

TL;DR

This paper extends Talenti-type comparison results for p-Laplace equations with Robin boundary conditions from the planar case to higher dimensions, under certain conditions on p, broadening the understanding of elliptic boundary value problems.

Contribution

It generalizes existing comparison results to higher dimensions for p-Laplace equations with Robin boundary conditions, including cases where p is small.

Findings

Point-wise comparison holds in any dimension for small p

Results extend previous planar case findings

Broadens applicability of comparison principles in elliptic PDEs

Abstract

In the last decades comparison results of Talenti type for Elliptic Problems with Dirichlet boundary conditions have been widely investigated. In this paper, we generalize the results obtained in arXiv:1909.11950 to the case of p-Laplace operator with Robin boundary conditions. The point-wise comparison, obtained in arXiv:1909.11950 only in the planar case, holds true in any dimension if p is sufficiently small.