Regularizing properties of the double layer potential of second order elliptic differential operators

We prove the validity of regularizing properties of a double layer potential associated to the fundamental solution of a nonhomogeneous second order elliptic differential operator with constant coefficients in Schauder spaces by exploiting an explicit formula for the tangential derivatives of the double layer potential itself. We also introduce ad hoc norms for kernels of integral operators in order to prove continuity results of integral operators upon variation of the kernel, which we apply to the layer potentials.