Classical solutions to integral equations with zero order kernels

Abstract

We show global and interior higher-order log-Hölder regularity estimates for solutions of Dirichlet integral equations where the operator has a nonintegrable kernel with a singularity at the origin that is weaker than that of any fractional Laplacian. As a consequence, under mild regularity assumptions on the right hand side, we show the existence of classical solutions of Dirichlet problems involving the logarithmic Laplacian and the logarithmic Schrödinger operator.

arXiv commentWe added a lower-order regularity estimate for the logarithmic Laplacian (Corollary 5.8)