  Segregated direct boundary-domain integral equations (BDIEs) based on a
parametrix and associated with the Dirichlet and Neumann boundary value
problems for the linear stationary diffusion partial differential equation with
a variable non-smooth (or limited-smoothness) coefficient on Lipschitz domains
are 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-normal
derivatives are well defined. Equivalence of the BDIEs to the original BVP,
BDIE solvability, solution uniqueness/non-uniqueness, as well as Fredholm
property and invertibility of the BDIE operators are analysed in appropriate
Sobolev spaces. It is shown that the BDIE operators for the Neumann BVP are not
invertible, however some finite-dimensional perturbations are constructed
leading to invertibility of the perturbed (stabilised) operators.
