CONTINUITY OF THE DOUBLE LAYER POTENTIAL OF A SECOND ORDER ELLIPTIC DIFFERENTIAL OPERATOR IN SCHAUDER SPACES ON THE BOUNDARY

Abstract

AbstractWe prove the validity of a regularizing property on the boundary of the double layer potential associated with the fundamental solution of a 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. Günter, S. Mikhlin, V.D. Kupradze, T.G. Gegelia, M.O. Basheleishvili and T.V. Burchuladze, U. Heinemann and extends the work of A. Kirsch who has considered the case of the Helmholtz operator.