A Rigidity Result for the Robin Torsion Problem

Abstract

Let $\Omega \subset {\mathbb{R}}^2$ be an open, bounded and Lipschitz set. We consider the torsion problem for the Laplace operator associated to $\Omega$ with Robin boundary conditions. In this setting, we study the equality case in the Talenti-type comparison, proved in arXiv:1909.11950. We prove that the equality is achieved only if $\Omega$ is a disk and the torsion function $u$ is radial.