REGULARITY OF THE SOLUTIONS OF ELLIPTIC-SYSTEMS IN POLYHEDRAL DOMAINS

The solution of the Dirichlet problem relative to an elliptic system i n a polyhedron has a complex singular behaviour near edges and vertice s. Here, we show that this solution has a global regularity in appropr iate weighted Sobolev spaces. Some useful embeddings of these spaces i nto classical Sobolev spaces are also established. As applications, we consider the Lame, Stokes and Navier-Stokes systems. The present resu lts will be applied in a forthcoming work to the constructive treatmen t of these problems by optimal convergent finite dement method.