Rigidity results for Serrin's overdetermined problems in Riemannian manifolds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916441343655936 |
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| author | Andrade, Maria Freitas, Allan Marín, Diego A. |
| author_facet | Andrade, Maria Freitas, Allan Marín, Diego A. |
| contents | In this work, we are interested in studying Serrin's overdetermined problems in Riemannian manifolds. For manifolds endowed with a conformal vector field, we prove a Pohozoaev-type identity to show a Serrin's type rigidity result using the P-function approach introduced by Weinberger. We proceed with a conformal change to achieve this goal, starting from a geometric Pohozaev identity due to Schoen. Moreover, we obtain a symmetry result for the associated Dirichlet problem by using a generalized normalized wall shear stress bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity results for Serrin's overdetermined problems in Riemannian manifolds Andrade, Maria Freitas, Allan Marín, Diego A. Differential Geometry Analysis of PDEs In this work, we are interested in studying Serrin's overdetermined problems in Riemannian manifolds. For manifolds endowed with a conformal vector field, we prove a Pohozoaev-type identity to show a Serrin's type rigidity result using the P-function approach introduced by Weinberger. We proceed with a conformal change to achieve this goal, starting from a geometric Pohozaev identity due to Schoen. Moreover, we obtain a symmetry result for the associated Dirichlet problem by using a generalized normalized wall shear stress bound. |
| title | Rigidity results for Serrin's overdetermined problems in Riemannian manifolds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2405.17312 |