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

RESUMO

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}.