ABSTRACT
Abstract As the main tool in the theory of difference potentials we split the difference potential on the boundary into a discrete single and double-layer potential. For a long time it was not possible to prove solvability conditions for Dirichlet problems based on discrete double-layer potentials. In this paper we show how we can overcome the difficulties. We prove that for arbitrarily chosen boundary values a unique solution of the interior and exterior discrete Dirichlet problems in the plane exists and describe this solution with the help of the discrete double-layer potential.
