Boundary-domain integral equations for variable coefficient Dirichlet BVP in 2D unbounded domain

Abstract

In this paper, the Dirichlet boundary value problem for the second order stationary diffusion elliptic partial differential equation with variable coefficient is considered in unbounded (exterior) two dimensional domain. Using an appropriate parametrix (Levi function), this problem is reduced to some direct segregated Boundary-Domain Integral Equations (BDIEs).We investigate the properties of corresponding parametrix-based integral volume and layer potentials in some weighted Sobolev spaces, as well as the unique sovability of BDIEs and their equivalence to the original BVP.