Regularity of viscosity solutions of the $σ_k$-Yamabe-type Problem for $k>n/2$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911952743170048 |
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| author | Wu, Jinyang |
| author_facet | Wu, Jinyang |
| contents | We study the regularity of Lipschitz viscosity solutions to the $σ_k$ Yamabe problem in the negative cone case. If either $k=n$ or the manifold is conformally flat and $k>n/2$, we prove that all Lipschitz viscosity solutions are smooth away from a closed set of measure zero. For the general $k>n/2$ case, under certain assumptions, we prove the existence of a Lipschitz viscosity solution that is smooth away from a closed set of measure zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity of viscosity solutions of the $σ_k$-Yamabe-type Problem for $k>n/2$ Wu, Jinyang Differential Geometry Analysis of PDEs 35J60, 35B65, 35D40, 53C18 We study the regularity of Lipschitz viscosity solutions to the $σ_k$ Yamabe problem in the negative cone case. If either $k=n$ or the manifold is conformally flat and $k>n/2$, we prove that all Lipschitz viscosity solutions are smooth away from a closed set of measure zero. For the general $k>n/2$ case, under certain assumptions, we prove the existence of a Lipschitz viscosity solution that is smooth away from a closed set of measure zero. |
| title | Regularity of viscosity solutions of the $σ_k$-Yamabe-type Problem for $k>n/2$ |
| topic | Differential Geometry Analysis of PDEs 35J60, 35B65, 35D40, 53C18 |
| url | https://arxiv.org/abs/2407.08300 |