A Rigidity Result for the Robin Torsion Problem

2022/09/14 by Alba Lia Masiello, Masiello, Alba Lia, Gloria Paoli +1
Mathematics · #35J05 #35J25 #46E30 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2209.06706

openalex publication_date 2022/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω⊂ ℝ² be an open, bounded and Lipschitz set. We consider the torsion problem for the Laplace operator associated to Ω 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 Ω is a disk and the torsion function u is radial.

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