DIRICHLET PROBLEMS IN POLYHEDRAL DOMAINS .1. REGULARITY OF THE SOLUTIONS

The solution of the Dirichlet problem relative to an elliptic operator in a polyhedron has a complex singular behaviour near edges and verti ces. Here we show that this solution and its conormal derivative have a global regularity in appropriate weighted Sobolev spaces. We also in vestigate some compact embeddings of these spaces. The present results will be applied in a forthcoming work to the constructive treatment o f the problem by optimal convergent finite element method and boundary element method.