Compact contact sets of sub-quadratic solutions to the thin obstacle problem
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909155132964864 |
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| author | Eberle, Simon Yu, Hui |
| author_facet | Eberle, Simon Yu, Hui |
| contents | We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution. On the other hand, if such a solution has a compact contact set, we show that it must be an ellipsoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03939 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compact contact sets of sub-quadratic solutions to the thin obstacle problem Eberle, Simon Yu, Hui Analysis of PDEs 35R35, 35B65 We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution. On the other hand, if such a solution has a compact contact set, we show that it must be an ellipsoid. |
| title | Compact contact sets of sub-quadratic solutions to the thin obstacle problem |
| topic | Analysis of PDEs 35R35, 35B65 |
| url | https://arxiv.org/abs/2304.03939 |