R\'egularit\'e du rayon hyperbolique

Satyanad Kichenassamy

doi:10.1016/j.crma.2003.10.037

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arXiv · 2507.03717

R\'egularit\'e du rayon hyperbolique

Satyanad Kichenassamy

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Abstract

Let $\Omega\subset\mathbb R^2$ be a bounded domain of class $C^{2+\alpha}$, $0<\alpha<1$. We show that if $u$ is the maximal solution of $\Delta u = 4\exp(2u)$, which tends to $+\infty$ as $(x,y)\to\partial\Omega$, then the hyperbolic radius $v=\exp(-u)$ is of class $C^{2+\alpha}$ up to the boundary. The proof relies on new Schauder estimates for Fuchsian elliptic equations.

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Satyanad Kichenassamy. 2025-07-04. R\'egularit\'e du rayon hyperbolique. https://doi.org/10.1016/j.crma.2003.10.037

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