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Comptes Rendus Mathématique
Volume 338, n° 1
pages 13-18 (janvier 2004)
Doi : 10.1016/j.crma.2003.10.037
Received : 26 October 2003 ; 
Régularité du rayon hyperbolique
Smoothness of hyperbolic radius

Satyanad  Kichenassamy
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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Soit   un domaine borné de classe  . On montre que si   est la solution maximale de  , qui tend vers   si  , alors le rayon hyperbolique   est de classe   jusqu'au bord. La démonstration repose sur de nouvelles estimations de Schauder pour des équations fuchsiennes elliptiques. Pour citer cet article : S. Kichenassamy, C. R. Acad. Sci. Paris, Ser. I 338 (2004).

Abstract

Let   be a bounded domain of class  . We show that if   is the maximal solution of  , which tends to   as  , then the hyperbolic radius   is of class   up to the boundary. The proof relies on new Schauder estimates for Fuchsian elliptic equations. To cite this article: S. Kichenassamy, C. R. Acad. Sci. Paris, Ser. I 338 (2004).




© 2003  Académie des sciences@@#104156@@

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