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arXiv · 2509.24557

On the Serrin's problem with Robin boundary conditions

Nunzia Gavitone·Riccardo Molinarolo
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Abstract

Let $\Omega \subset \mathbb{R}^N$, $N\ge 2$, be an open, connected, bounded set with $C^2$ boundary. In this paper we consider the torsion problem with Robin boundary conditions and we study the symmetry of the solutions when suitable extra conditions are imposed on the boundary of $\Omega$. In particular, we prove the Serrin's rigidity result under suitable assumptions on the domain and on the Robin parameter.

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Nunzia Gavitone, Riccardo Molinarolo. 2025-09-29. On the Serrin's problem with Robin boundary conditions. https://arxiv.org/abs/2509.24557

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