Serrin-type problem in divergence form on Riemannian manifolds

Márcio Batista; Márcio Santos; Antônio da Silva; Joyce Sindeaux

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arXiv · 2507.17838

Serrin-type problem in divergence form on Riemannian manifolds

Márcio Batista·Márcio Santos·Antônio da Silva·Joyce Sindeaux

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Abstract

In this paper, we investigate an overdetermined boundary value problem of divergence type on bounded domains in Riemannian manifolds with non-negative Ricci curvature. Using integral identities and the $P$-function method, we derive geometric inequalities and rigidity results. Under natural conditions on the nonlinearity, we prove that equality implies the domain is isometric to a Euclidean ball, thereby extending classical symmetry results to the Riemannian setting.

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BibTeX RIS

Márcio Batista, Márcio Santos, Antônio da Silva, Joyce Sindeaux. 2025-07-23. Serrin-type problem in divergence form on Riemannian manifolds. https://arxiv.org/abs/2507.17838

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