A Rigidity Result for the Robin Torsion Problem

Abstract

AbstractLet$$\Omega \subset \mathbb {R}^2$$Ω⊂R2be an open, bounded and Lipschitz set. We consider the torsion problem for the Laplace operator associated to$$\Omega $$Ωwith Robin boundary conditions. In this setting, we study the equality case in the Talenti-type comparison, proved in Alvino et al. (Commun Pure Appl Math 76:585–603, 2023).. We prove that the equality is achieved only if$$\Omega $$Ωis a disk and the torsion functionuis radial.