A New Family of Boundary-Domain Integral Equations for a Mixed Elliptic BVP with Variable Coefficient

Abstract

A mixed boundary value problem for the stationary heat transfer partial differential equation with variable coefficient is reduced to some systems of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We use a parametrix different from the one employed by Mikhailov (2002) and Chkadua, Mikhailov, Natroshvili (2009). Mapping properties of the potential type integral operators appearing in these equations are presented in appropriate Sobolev spaces. 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.