Comptes Rendus
no. 3
Partial Differential Equations
Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains
[Formules asymptotiques uniformes pour des noyaux de Green dans des domaines avec perturbations regulières et singulières]

Présenté par : 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.

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.

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.

Reçu le :
Accepté le :
Publié le :
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 
@article{CRMATH_2006__343_3_185_0,
     author = {Vladimir Maz'ya and Alexander Movchan},
     title = {Uniform asymptotic formulae for {Green's} kernels in regularly and singularly perturbed domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {185--190},
     publisher = {Elsevier},
     volume = {343},
     number = {3},
     year = {2006},
     doi = {10.1016/j.crma.2006.05.015},
     language = {en},
}
TY  - JOUR
AU  - Vladimir Maz'ya
AU  - Alexander Movchan
TI  - Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 185
EP  - 190
VL  - 343
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crma.2006.05.015
LA  - en
ID  - CRMATH_2006__343_3_185_0
ER  - 
%0 Journal Article
%A Vladimir Maz'ya
%A Alexander Movchan
%T Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains
%J Comptes Rendus. Mathématique
%D 2006
%P 185-190
%V 343
%N 3
%I Elsevier
%R 10.1016/j.crma.2006.05.015
%G en
%F CRMATH_2006__343_3_185_0
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/

[1] D. Fujiwara; S. Ozawa The Hadamard variational formula for the Green functions of some normal elliptic boundary value problems, Proc. Japan Acad. Ser. A Math. Sci., Volume 54 (1978) no. 8, pp. 215-220

[2] J. Hadamard, Sur le problème d'analyse relatif à l'équilibre des plaques élastiques encastrées, Mémoire couronné en 1907 par l'Académie des Sciences 33 (4) 515–629

[3] P. Levy Leçons d'analyse fonctionnelle, Gauthier-Villars, Paris, 1922

[4] V. Maz'ya; S. Nazarov; B. Plamenevskij Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, vols. 1–2, Birkhäuser, 2000

[5] S. Ozawa Perturbation of domains and Green kernels of heat equations, Proc. Japan Acad. Ser. A Math. Sci., Volume 54 (1978), pp. 322-325 Part II, 55 (1979) 172–175; Part III, 55 (1979) 227–230

[6] S. Ozawa Spectra of the Laplacian with small Robin conditional boundary, Proc. Japan Acad. Ser. A Math. Sci., Volume 72 (1996) no. 3, pp. 53-54

[7] S. Ozawa; S. Roppongi Heat kernel and singular variation of domains, Osaka J. Math., Volume 32 (1995) no. 4, pp. 941-957

Cité par Sources :

Commentaires - Politique