[Régularité anisotrope pour le Laplacien et l'opérateur de Maxwell dans un polyèdre]
Nous choisissons d'étudier le problème de Dirichlet pour le Laplacien et le problème de Maxwell électrique, comme représentants de classes plus larges de problèmes intéressant la modélisation de phénomènes physiques stationnaires. Nous énonçons des résultats de régularité dans deux familles d'espaces de Sobolev à poids : l'une, classique, isotrope, et l'autre, nouvelle, anisotrope, où l'on tient compte de l'hypoellipticité le long des arêtes d'un domaine polyédral.
As representatives of a larger class of elliptic boundary value problems of mathematical physics, we study the Dirichlet problem for the Laplace operator and the electric boundary problem for the Maxwell operator. We state regularity results in two families of weighted Sobolev spaces: A classical isotropic family, and a new anisotropic family, where the hypoellipticity along an edge of a polyhedral domain is taken into account.
Accepté le :
Publié le :
Annalisa Buffa 1 ; Martin Costabel 2 ; Monique Dauge 2
@article{CRMATH_2003__336_7_565_0,
author = {Annalisa Buffa and Martin Costabel and Monique Dauge},
title = {Anisotropic regularity results for {Laplace} and {Maxwell} operators in a polyhedron},
journal = {Comptes Rendus. Math\'ematique},
pages = {565--570},
publisher = {Elsevier},
volume = {336},
number = {7},
year = {2003},
doi = {10.1016/S1631-073X(03)00138-9},
language = {en},
}
TY - JOUR AU - Annalisa Buffa AU - Martin Costabel AU - Monique Dauge TI - Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron JO - Comptes Rendus. Mathématique PY - 2003 SP - 565 EP - 570 VL - 336 IS - 7 PB - Elsevier DO - 10.1016/S1631-073X(03)00138-9 LA - en ID - CRMATH_2003__336_7_565_0 ER -
Annalisa Buffa; Martin Costabel; Monique Dauge. Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron. Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 565-570. doi : 10.1016/S1631-073X(03)00138-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00138-9/
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