Rigidity results via a Poincaré type formula for stable solutions of quasilinear anisotropic elliptic equations

Abstract

In this paper we prove some one-dimensional symmetry results for stable solutions to quasilinear anisotropic elliptic equations in ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$. In this regard, we give an extension of a formula obtained in \cite{SZ1,SZ2, FSV}. The techniques used are inspired by the works of \cite{Fhdr,FSV}.

To appear on JDE