Analysis of boundary-domain integral equations based on a new parametrix for the mixed diffusion BVP with variable coefficient in an interior Lipschitz domain

Abstract

A mixed boundary value problem for the partial differential equation of diffusion in an inhomogeneous medium in a Lipschitz domain is reduced to a system of direct segregated parametrix-based boundary-domain integral equations (BDIEs). We use a parametrix different from the one employed in previous papers by Mikhailov (2002, 2006) and Chkadua, Mikhailov and Natroshvili (2009). We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.