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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.02845 |
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| _version_ | 1866911876959436800 |
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| author | Magnanini, Rolando Molinarolo, Riccardo Poggesi, Giorgio |
| author_facet | Magnanini, Rolando Molinarolo, Riccardo Poggesi, Giorgio |
| contents | We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that the first and third authors previously proved and used to obtain quantitative estimates of spherical symmetry for the Serrin overdetermined boundary value problem. As an application, we prove a quantitative symmetry result for the reverse Serrin problem, which we introduce for the first time in this paper. In passing, we obtain a rigidity result for solutions of the aforementioned Poisson equation subject to a constant Neumann condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A general integral identity with applications to a reverse Serrin problem Magnanini, Rolando Molinarolo, Riccardo Poggesi, Giorgio Analysis of PDEs We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that the first and third authors previously proved and used to obtain quantitative estimates of spherical symmetry for the Serrin overdetermined boundary value problem. As an application, we prove a quantitative symmetry result for the reverse Serrin problem, which we introduce for the first time in this paper. In passing, we obtain a rigidity result for solutions of the aforementioned Poisson equation subject to a constant Neumann condition. |
| title | A general integral identity with applications to a reverse Serrin problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.02845 |