Boundary-domain integral equations for Dirichlet diffusion problems with non-smooth coefficient

Abstract

We obtain a system of boundary-domain integral equations (BDIE) equivalent to the Dirichlet problem for the diffusion equation in non-homogeneous media. We use an extended version of the boundary integral method for PDEs with variable coefficients for which a parametrix is required. We generalize existing results for this family of parametrices considering a non-smooth variable coefficient in the PDE and source term in \(H^{s-2}(\Omega)\), \(1/2< s <3/2\) defined on a Lipschitz domain. The main results concern the equivalence between the original BVP and the corresponding BDIE system, as well as the well-posedness of the BDIE system