Optimal boundary regularity for mixed local and nonlocal equations
Analysis of PDEs
2025-12-10 v2
Abstract
We provide sharp boundary regularity estimates for solutions to elliptic equations driven by an integro-differential operator obtained as the sum of a Laplacian with a nonlocal operator generalizing a fractional Laplacian. Our approach makes use of weighted H\"older spaces as well as regularity estimates for the Laplacian in this context and a fixed-point argument. We show the optimality of the obtained estimates by means of a counterexample that we have striven to keep as explicit as possible.
Cite
@article{arxiv.2507.13711,
title = {Optimal boundary regularity for mixed local and nonlocal equations},
author = {Nicola Abatangelo and Elisa Affili and Matteo Cozzi},
journal= {arXiv preprint arXiv:2507.13711},
year = {2025}
}
Comments
34 pages, 1 figure