Comptes Rendus
no. 7
Partial Differential Equations
Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron
[Régularité anisotrope pour le Laplacien et l'opérateur de Maxwell dans un polyèdre]

Présenté par : Philippe G. Ciarlet

Annalisa Buffa1 ; Martin Costabel2 ; Monique Dauge2
1 IMATI-CNR, Pavia, Italy
2 Irmar, Université de Rennes 1, France
Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 565-570.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00138-9
Annalisa Buffa 1 ; Martin Costabel 2 ; Monique Dauge 2

1 IMATI-CNR, Pavia, Italy
2 Irmar, Université de Rennes 1, France 
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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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