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

Francesco Dondi, Massimo Lanza de Cristoforis

Published 2021-03-11Version 1

We prove the validity of regularizing properties of a double layer potential associated to the fundamental solution of a {\em 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 layer potentials.