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Segregated direct boundary-domain integral equations (BDIEs) based on aparametrix and associated with the Dirichlet and Neumann boundary valueproblems for the linear stationary diffusion partial differential equation witha variable non-smooth (or limited-smoothness) coefficient on Lipschitz domainsare formulated. The PDE right hand sides belong to the Sobolev(Bessel-potential) space $H^{s-2}(\Omega)$ or $\widetilde H^{s-2}(\Omega)$,$1/2<s<3/2$, when neither strong classical nor weak canonical co-normalderivatives are well defined. Equivalence of the BDIEs to the original BVP,BDIE solvability, solution uniqueness/non-uniqueness, as well as Fredholmproperty and invertibility of the BDIE operators are analysed in appropriateSobolev spaces. It is shown that the BDIE operators for the Neumann BVP are notinvertible, however some finite-dimensional perturbations are constructedleading to invertibility of the perturbed (stabilised) operators.

Analysis of Segregated Boundary-Domain Integral Equations for BVPs with Non-smooth Coefficient on Lipschitz Domains