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Comptes Rendus Mathématique
Volume 343, n° 3
pages 185-190 (août 2006)
Doi : 10.1016/j.crma.2006.05.015
Received : 13 December 2005 ;  accepted : 15 May 2006
Uniform asymptotic formulae for Greenʼs kernels in regularly and singularly perturbed domains
Formules asymptotiques uniformes pour des noyaux de Green dans des domaines avec perturbations regulières et singulières
 

Vladimir Mazʼya a, b, c , Alexander Movchan a
a Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK 
b Department of Mathematics, Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, USA 
c Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden 

Abstract

Asymptotic formulae for Greenʼs kernels   of various boundary value problems for the Laplace operator are obtained in regularly perturbed domains and certain domains with small singular perturbations of the boundary, as  . The main new feature of these asymptotic formulae is their uniformity with respect to the independent variables x and y. To cite this article: V. Mazʼya, A. Movchan, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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

Des formules asymptotiques sont obtenues pour des noyaux de Green   de divers problèmes aux limites pour lʼopérateur de Laplace dans des domaines régulièrement perturbés et certains domaines avec des petites perturbations singulières du bord, quand  . Le caractère novateur de ces formules asymptotiques réside dans leur uniformité par rapport aux variables indépendantes x et y. Pour citer cet article : V. Mazʼya, A. Movchan, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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


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