Serrin-type problem in divergence form on Riemannian manifolds
Differential Geometry
2025-07-25 v1
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 -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.
Cite
@article{arxiv.2507.17838,
title = {Serrin-type problem in divergence form on Riemannian manifolds},
author = {Márcio Batista and Márcio Santos and Antônio da Silva and Joyce Sindeaux},
journal= {arXiv preprint arXiv:2507.17838},
year = {2025}
}