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arXiv · 2209.06706

A Rigidity Result for the Robin Torsion Problem

Alba Lia Masiello·Gloria Paoli
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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.

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Alba Lia Masiello, Gloria Paoli. 2022-09-14. A Rigidity Result for the Robin Torsion Problem. https://arxiv.org/abs/2209.06706

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