Équations aux dérivées partielles
Régularité du rayon hyperbolique
[Smoothness of hyperbolic radius]
Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 13-18.

Let Ω 2 be a bounded domain of class C 2+α ,0<α<1. We show that if u is the maximal solution of Δu=4exp(2u), which tends to +∞ as (x,y)Ω, then the hyperbolic radius v=exp(−u) is of class C2+α up to the boundary. The proof relies on new Schauder estimates for Fuchsian elliptic equations.

Soit Ω 2 un domaine borné de classe C 2+α ,0<α<1. On montre que si u est la solution maximale de Δu=4exp(2u), qui tend vers +∞ si (x,y)Ω, alors le rayon hyperbolique v=exp(−u) est de classe C2+α jusqu'au bord. La démonstration repose sur de nouvelles estimations de Schauder pour des équations fuchsiennes elliptiques.

Received:
Published online:
DOI: 10.1016/j.crma.2003.10.037
Kichenassamy, Satyanad 1

1 Laboratoire de mathématiques (UMR 6056), CNRS & Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims cedex 2, France
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Kichenassamy, Satyanad. Régularité du rayon hyperbolique. Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 13-18. doi : 10.1016/j.crma.2003.10.037. http://www.numdam.org/articles/10.1016/j.crma.2003.10.037/

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