Coefficient formulae for asymptotic expansions of solutions of elliptic boundary value problems near conical points

Abstract

It is well known that singularities are present in solutions of elliptic boundary value problems in domains with conical boundary points. The solution consists of singular terms, which appear in a neighbourhood of a conical point, and a more regular term. The coefficients of the singular terms, the so-called stress intensity factors, are especially of interest for applications. We describe a method, how some of them may be calculated, if the right hand sides are from standard Sobolev spaces. In some cases the coefficients are unstable and a stabilization procedure is necessary.We handle as examples boundary value problems for the Laplace equation in two and three dimensional domains.