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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 891-896 (août 2010)
Doi : 10.1016/j.crma.2010.06.024
Received : 19 April 2010 ;  accepted : 29 June 2010
Expansion of the Green's function for divergence form operators
Expansion de la fonction de Green pour les opérateurs de type divergence
 

Saïma Khenissy a , Yomna Rébaï b , Dong Ye c
a Département de mathématiques appliquées, institut supérieur d'informatique, 2037 Ariana, Tunisia 
b Département de mathématiques, faculté des sciences de Bizerte, Jarzouna, 7021 Bizerte, Tunisia 
c LMAM, UMR 7122, Université de Metz, 57045 Metz, France 

Abstract

We consider the fundamental solution   of the operator   on a bounded smooth domain   ( ), associated to the Dirichlet boundary condition, where a is a positive smooth function on  . In this short Note, we give a precise description of the function  . In particular, we define in a unique way its continuous part   and we prove that the corresponding Robin's function   belongs to  , although   in general.

The full text of this article is available in PDF format.
Résumé

On considère la solution fondamentale   de l'opérateur  , sur un domaine borné régulier   ( ) avec les conditions de Dirichlet au bord, ici a est une fonction régulière et strictement positive sur  . Dans cette Note, on donne une description précise de la fonction  . On définit notamment  , la partie continue de   et on montre que la fonction de Robin correspondante   est dans  , sachant que   en général.

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