Francesco Dondi and Massimo Lanza de Cristoforis
abstract:
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.
Mathematics Subject Classification: 31B10
Key words and phrases: Double layer potential, second order differential operators with constant coefficients