On the Behaviour of Solutions to the Dirichiet Problem for Second Order Elliptic Equations near Edges and Polyhedral Vertices with Critical Angles

Abstract

The Dirichiet problem for second order elliptic equations will be considered in domains of ${\mathbb{R}}^N$ with smooth ($N-2$)-dimensional edges at the boundary. The authors get the asymptotical decomposition of the solution near edges with angles running through a critical value. Furthermore, the first terms of the asymptotics of the solution near a polyhedral vertex are given for a domain with critical angle $\pi$/2 in the vertex.