Classical solutions to integral equations with zero order kernels
Analysis of PDEs
2022-10-05 v3
Abstract
We show global and interior higher-order log-H\"older 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 Schr\"odinger operator.
Cite
@article{arxiv.2208.12841,
title = {Classical solutions to integral equations with zero order kernels},
author = {Héctor A. Chang-Lara and Alberto Saldaña},
journal= {arXiv preprint arXiv:2208.12841},
year = {2022}
}
Comments
We added a lower-order regularity estimate for the logarithmic Laplacian (Corollary 5.8)