One-phase Free Boundary Problems on RCD Metric Measure Spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866918457897910272 |
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| author | Chan, Chung-Kwong Zhang, Hui-Chun Zhu, Xi-Ping |
| author_facet | Chan, Chung-Kwong Zhang, Hui-Chun Zhu, Xi-Ping |
| contents | In this paper, we consider a vector-valued one-phase Bernoulli-type free boundary problem on a metric measure space $(X,d,μ)$ with Riemannian curvature-dimension condition $RCD(K,N)$. We first prove the existence and the local Lipschitz regularity of the solutions, provided that the space $X$ is non collapsed, i.e. $μ$ is the $N$-dimensional Hausdorff measure of $X$. And then we show that the free boundary of the solutions is an $(N-1)$-dimensional topological manifold away from a relatively closed subset of Hausdorff dimension $\leqslant N-3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_06962 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | One-phase Free Boundary Problems on RCD Metric Measure Spaces Chan, Chung-Kwong Zhang, Hui-Chun Zhu, Xi-Ping Analysis of PDEs Differential Geometry Metric Geometry In this paper, we consider a vector-valued one-phase Bernoulli-type free boundary problem on a metric measure space $(X,d,μ)$ with Riemannian curvature-dimension condition $RCD(K,N)$. We first prove the existence and the local Lipschitz regularity of the solutions, provided that the space $X$ is non collapsed, i.e. $μ$ is the $N$-dimensional Hausdorff measure of $X$. And then we show that the free boundary of the solutions is an $(N-1)$-dimensional topological manifold away from a relatively closed subset of Hausdorff dimension $\leqslant N-3$. |
| title | One-phase Free Boundary Problems on RCD Metric Measure Spaces |
| topic | Analysis of PDEs Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2112.06962 |