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arXiv · 2506.00697

Overdetermined elliptic problems on model Riemannian manifolds

João Marcos do Ó·Jaqueline de Lima·Márcio Santos
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Abstract

We establish a rigidity theorem for annular sector-like domains in the setting of overdetermined elliptic problems on model Riemannian manifolds. Specifically, if such a domain admits a solution to the inhomogeneous Helmholtz equation satisfying both constant Dirichlet and constant Neumann boundary conditions, then the domain must be a spherical sector, and the solution must be radially symmetric. This result underscores the strong geometric constraints imposed by overdetermined boundary conditions, extending classical rigidity phenomena to this more general framework.

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João Marcos do Ó, Jaqueline de Lima, Márcio Santos. 2025-05-31. Overdetermined elliptic problems on model Riemannian manifolds. https://arxiv.org/abs/2506.00697

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