On the Serrin's problem with Robin boundary conditions

Q: What type of study is this?

This is a Quantitative Study study.

Nunzia Gavitone; Riccardo Molinarolo

doi:10.48550/arxiv.2509.24557

September 29, 2025Open Access

On the Serrin's problem with Robin boundary conditions

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Key Points

Symmetry of solutions is proven for the torsion problem under Robin boundary conditions, enhancing understanding of boundary interactions.
Key findings include proving Serrin's rigidity result contingent on specific assumptions related to the domain and Robin parameters.
The study focuses on bounded sets in higher dimensions, establishing crucial relationships between the geometry of the domain and solution behavior.
Establishing the conditions on the boundary contributes to the broader applicability of Serrin's results in mathematical physics and engineering.

Implication

Analysis reveals symmetry outcomes in solutions to torsion problems with Robin boundary conditions, indicating rigidity under specific conditions.

Abstract

Let Ω⊂ RN, N≥ 2, be an open, connected, bounded set with C² 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 $Ω$. In particular, we prove the Serrin's rigidity result under suitable assumptions on the domain and on the Robin parameter.

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Cite This Study

Gavitone et al. (2025) studied this question.

synapsesocial.com/papers/68f5fcce8d54a28a75cf1c60 https://doi.org/10.48550/arxiv.2509.24557

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On the Serrin's problem with Robin boundary conditions

Key Points

Implication

Abstract

Discussion

Cite This Study

On the Serrin's problem with Robin boundary conditions

Key Points

Implication

Abstract

Discussion

Cite This Study

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