Level sets of solutions to the stationary Hamilton-Jacobi equation are John regular
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908645741035520 |
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| author | Davoli, Elisa Stefanelli, Ulisse |
| author_facet | Davoli, Elisa Stefanelli, Ulisse |
| contents | Let $u$ be the unique nonnegative viscosity solution of the Hamilton-Jacobi equation $H(x,\nabla u)=0$ in the external domain ${\mathbb R}^{ n} \setminus K$ with $u=0$ on $K$. Under general conditions on $H$, we prove that all sublevels of $u$ are John domains. Moreover, if $K$ itself is a John domain, we provide a uniform lower bound on the John constant of all sublevels. We exhibit counterexamples showing that John regularity is sharp in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17635 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Level sets of solutions to the stationary Hamilton-Jacobi equation are John regular Davoli, Elisa Stefanelli, Ulisse Analysis of PDEs 35F21, 35B65 Let $u$ be the unique nonnegative viscosity solution of the Hamilton-Jacobi equation $H(x,\nabla u)=0$ in the external domain ${\mathbb R}^{ n} \setminus K$ with $u=0$ on $K$. Under general conditions on $H$, we prove that all sublevels of $u$ are John domains. Moreover, if $K$ itself is a John domain, we provide a uniform lower bound on the John constant of all sublevels. We exhibit counterexamples showing that John regularity is sharp in this setting. |
| title | Level sets of solutions to the stationary Hamilton-Jacobi equation are John regular |
| topic | Analysis of PDEs 35F21, 35B65 |
| url | https://arxiv.org/abs/2312.17635 |