Decompositions in Edge and Corner Singularities for the Solution of the Dirichlet Problem of the Laplacian in a Polyhedron

Abstract

AbstractThe solution of the three‐dimensional Dirichlet problem for the Laplacian in a polyhedral domain has Special singular forms at corners and edges. The main result of this paper is a “tensor‐product” decomposition of those singular forms along the edges. Such a decomposition with both edge singularities, additional corner singularities and a smoother remainder refines known regularity results for the solution where either the edge singularities are of non‐tensor product form or the remainder term belongs to an anisotropic Sobolev space for data given in an isotropic Sobolev space.