Régularité du rayon hyperbolique
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912466029510656 |
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| author | Kichenassamy, Satyanad |
| author_facet | Kichenassamy, Satyanad |
| contents | Let $Ω\subset\mathbb R^2$ be a bounded domain of class $C^{2+α}$, $0<α<1$. We show that if $u$ is the maximal solution of $Δu = 4\exp(2u)$, which tends to $+\infty$ as $(x,y)\to\partialΩ$, then the hyperbolic radius $v=\exp(-u)$ is of class $C^{2+α}$ up to the boundary. The proof relies on new Schauder estimates for Fuchsian elliptic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Régularité du rayon hyperbolique Kichenassamy, Satyanad Analysis of PDEs Complex Variables Functional Analysis Let $Ω\subset\mathbb R^2$ be a bounded domain of class $C^{2+α}$, $0<α<1$. We show that if $u$ is the maximal solution of $Δu = 4\exp(2u)$, which tends to $+\infty$ as $(x,y)\to\partialΩ$, then the hyperbolic radius $v=\exp(-u)$ is of class $C^{2+α}$ up to the boundary. The proof relies on new Schauder estimates for Fuchsian elliptic equations. |
| title | Régularité du rayon hyperbolique |
| topic | Analysis of PDEs Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2507.03717 |