## Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron

*
Annalisa Buffa,
Martin Costabel,
Monique Dauge*

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

**Finite Element Method based on anisotropic meshes**
* (paper by the same authors). *

March 2003.

*C. R. Acad. Sci. Paris Ser. I* ** 336 ** (2003) 565-570.