Asymptotics of the Solution of a Boundary Integral Equation Under a Small Perturbation of a Corner

Abstract

The boundary integral equation of the Dirichlet problem is considered in a plane domain with a smooth boundary which is a small perturbation of a contour with an angular point. The asymptotics of the solution are given with respect to a perturbation parameter $ϵ$. The problem studied in this article serves as an example of the use of a general method which is also applicable to the three-dimensional case, to the Neumann problem and to problems of hydrostatics and elasticity.