This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2013 World Scientific Publishing.Direct segregated systems of boundary-domain integral equations are formulated for the mixed (Dirichlet–Neumann) boundary value problems for a scalar second-order divergent elliptic partial differential equation with a variable coefficient in an exterior three-dimensional domain. The boundary-domain integral equation system equivalence to the original boundary value problems and the Fredholm properties and invertibility of the corresponding boundary-domain integral operators are analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on the corresponding properties of the BVPs in weighted Sobolev spaces that are proved as well.The work was supported by the grant EP/H020497/1 \Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients" of the EPSRC, UK
