Régularité anisotrope pour le Laplacien et l'opérateur de Maxwell dans un polyèdre

Abstract

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. © 2003 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All rights reserved.