A new family of boundary-domain integral equations for the Dirichlet Problem of the diffusion equation in nhomogeneous media with H −1 (Ω) source term on Lipschitz Domains

The interior Dirichlet boundary value problem for the diffusion equation in nonhomogeneous media is reduced to a system of Boundary-Domain Integral Equations (BDIEs) employing the parametrix obtained in 1 different from2. We further extend the results obtained in 1 for the mixed problem in a smooth domain with L²(Ω) hand side to Lipschitz domains and PDE right-hand in the Sobolev space H¯(Ω), where neither the classical nor the canonical co-normal derivatives are well defined. Equivalence between the system of BDIEs and the original BVP is proved along with their solvability and solution uniqueness in appropriate Sobolev spaces