Overdetermined elliptic problems on model Riemannian manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908388058726400 |
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| author | Ó, João Marcos do de Lima, Jaqueline Santos, Márcio |
| author_facet | Ó, João Marcos do de Lima, Jaqueline Santos, Márcio |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_00697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Overdetermined elliptic problems on model Riemannian manifolds Ó, João Marcos do de Lima, Jaqueline Santos, Márcio Analysis of PDEs Differential Geometry 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. |
| title | Overdetermined elliptic problems on model Riemannian manifolds |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2506.00697 |