Continuity of the double layer potential of a second order elliptic differential operator in Schauder spaces on the boundary

Abstract

We prove the validity of a regularizing property on the boundary of the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator with constant coefficients in Schauder spaces of exponent greater or equal to two that sharpens classical results of N.M.~G\"{u}nter, S.~Mikhlin, V.D.~Kupradze, T.G.~Gegelia, M.O.~Basheleishvili and T.V.~Bur\-chuladze, U.~Heinemann and extends the work of A.~Kirsch who has considered the case of the Helmholtz operator.