As representatives of wider classes of elliptic boundary value problems connected to physical models, we consider 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 of Kondrat'ev type, and a new anisotropic family, where the hypoellipticity along an edge of a polyhedral domain is taken into account.
These results are used to bound the approximation error in a
(paper by the same authors).
C. R. Acad. Sci. Paris Ser. I 336 (2003) 565-570.
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