Regularity of the solutions of elliptic systems in polyhedral domains

Abstract

The solution of the Dirichlet problem relative to an elliptic system in a polyhedron has a complex singular behaviour near edges and vertices. Here, we show that this solution has a global regularity in appropriate weighted Sobolev spaces. Some useful embeddings of these spaces into classical Sobolev spaces are also established. As applications, we consider the Lam e, Stokes and Navier-Stokes systems. The present results will be applied in a forthcoming work to the constructive treatment of these problems by optimal convergent nite element method.