@article{Abatangelo2026, 
author = {Nicola Abatangelo and Elisa Affili and Matteo Cozzi},
title = {Optimal boundary regularity for mixed local and nonlocal equations},
year = {2026},
journal = {Mathematics in Engineering},
volume = {8},
number = {1},
pages = {1-42},
keywords = {elliptic regularity, mixed operators, weighted Hölder spaces, boundary value problems, nonlocal operators, fractional Laplacian},
url = {https://www.sciopen.com/article/10.3934/mine.2026001},
doi = {10.3934/mine.2026001},
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 Hölder 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.}
}