Comptes Rendus
no. 3
Partial Differential Equations
Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains

Presented by: Évariste Sanchez Palencia

Vladimir Maz'ya1, 2, 3; Alexander Movchan1
1 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
2 Department of Mathematics, Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, USA
3 Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Comptes Rendus. Mathématique, Volume 343 (2006) no. 3, pp. 185-190.

Asymptotic formulae for Green's kernels Gε(x,y) 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 ε→0. The main new feature of these asymptotic formulae is their uniformity with respect to the independent variables x and y.

Des formules asymptotiques sont obtenues pour des noyaux de Green Gε(x,y) de divers problèmes aux limites pour l'opérateur de Laplace dans des domaines régulièrement perturbés et certains domaines avec des petites perturbations singulières du bord, quand ε→0. Le caractère novateur de ces formules asymptotiques réside dans leur uniformité par rapport aux variables indépendantes x et y.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.05.015

Vladimir Maz'ya 1, 2, 3; Alexander Movchan 1

1 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
2 Department of Mathematics, Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, USA
3 Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden 
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Vladimir Maz'ya; Alexander Movchan. Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains. Comptes Rendus. Mathématique, Volume 343 (2006) no. 3, pp. 185-190. doi : 10.1016/j.crma.2006.05.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.05.015/

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