A Rigidity Result for the Robin Torsion Problem
Alba Lia Masiello, Gloria Paoli · Journal of Geometric Analysis · 2023
Abstract Let $$\Omega \subset \mathbb {R}^2$$ Ω⊂R2 be an open, bounded and Lipschitz set. We consider the torsion problem for the Laplace operator associated to $$\Omega $$ Ω with 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 $$\Omega $$ Ω is a disk and the torsion functionuis radial.