Qualitative properties of free boundaries for the exterior Bernoulli problem for the half Laplacian
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916555517853696 |
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| author | Jarohs, Sven Kulczycki, Tadeusz Salani, Paolo |
| author_facet | Jarohs, Sven Kulczycki, Tadeusz Salani, Paolo |
| contents | In this work, we study the asymptotic behavior of the free boundary of the solution to the exterior Bernoulli problem for the half Laplacian when the Bernoulli's gradient parameter tends to $0^+$ and to $+\infty$. Moreover, we show that, under suitable conditions, the perpendicular rays of the free boundary always meet the convex envelope of the fixed boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Qualitative properties of free boundaries for the exterior Bernoulli problem for the half Laplacian Jarohs, Sven Kulczycki, Tadeusz Salani, Paolo Analysis of PDEs 35R35, 35S99 In this work, we study the asymptotic behavior of the free boundary of the solution to the exterior Bernoulli problem for the half Laplacian when the Bernoulli's gradient parameter tends to $0^+$ and to $+\infty$. Moreover, we show that, under suitable conditions, the perpendicular rays of the free boundary always meet the convex envelope of the fixed boundary. |
| title | Qualitative properties of free boundaries for the exterior Bernoulli problem for the half Laplacian |
| topic | Analysis of PDEs 35R35, 35S99 |
| url | https://arxiv.org/abs/2409.17810 |