On Dirichlet’s Problem for Elliptic Equations in Sectionally Smooth n-Dimensional Domains

Abstract

This paper is concerned with the first boundary value problem for linear second order elliptic equations in a domain $\Omega \in R^n (n \geqq 2)$ with edges on its boundary. Conditions sufficient for the solution u to be in $C_\nu (\bar \Omega ),1 < \nu < 2$, are given. Further statements concern the nature of singularities which the second partial derivatives of the solution may have at the edges.