Asymptotics of the Solution of an Integral Equation to Transmission Problems with Singular Perturbed Boundary

Abstract

The integral equation to a transmission problem of the Laplacian is considered on a smooth boundary of a plane domain. The contour depends on a positive parameter e and the domain has a corner in the limit case $ϵ=0$. The main terms of an asymptotic expansion showing the influence of the parameter are given. The remaining part is estimated in a weak norm.