Face 2-phase: how much overdetermination is enough to get symmetry in two-phase problems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912364974047232 |
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| author | Cavallina, Lorenzo Poggesi, Giorgio |
| author_facet | Cavallina, Lorenzo Poggesi, Giorgio |
| contents | We provide a full characterization of multi-phase problems under a large class of overdetermined Serrin-type conditions. Our analysis includes both symmetry and asymmetry (including bifurcation) results. A broad range of techniques is needed to obtain a full characterization of all the cases, including applications of results obtained via the moving planes method, approaches via integral identities in the wake of Weinberger, applications of the Crandall-Rabinowitz theorem, and the Chauchy-Kovalevskaya theorem. The multi-phase setting entails intrinsic difficulties that make it difficult to predict whether a given overdetermination will lead to symmetry or asymmetry results; the results of our analysis are significant as they answer such a question providing a full characterization of both symmetry and asymmetry results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_11088 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Face 2-phase: how much overdetermination is enough to get symmetry in two-phase problems Cavallina, Lorenzo Poggesi, Giorgio Analysis of PDEs 35B35, 35J15, 35N25, 35Q93 We provide a full characterization of multi-phase problems under a large class of overdetermined Serrin-type conditions. Our analysis includes both symmetry and asymmetry (including bifurcation) results. A broad range of techniques is needed to obtain a full characterization of all the cases, including applications of results obtained via the moving planes method, approaches via integral identities in the wake of Weinberger, applications of the Crandall-Rabinowitz theorem, and the Chauchy-Kovalevskaya theorem. The multi-phase setting entails intrinsic difficulties that make it difficult to predict whether a given overdetermination will lead to symmetry or asymmetry results; the results of our analysis are significant as they answer such a question providing a full characterization of both symmetry and asymmetry results. |
| title | Face 2-phase: how much overdetermination is enough to get symmetry in two-phase problems |
| topic | Analysis of PDEs 35B35, 35J15, 35N25, 35Q93 |
| url | https://arxiv.org/abs/2312.11088 |