Gradient regularity and first-order potential estimates for a class of nonlocal equations
Analysis of PDEs
2024-10-29 v2
Abstract
We consider nonlocal equations of order larger than one with measure data and prove gradient regularity in Sobolev and H\"older spaces as well as pointwise bounds of the gradient in terms of Riesz potentials, leading to fine regularity results in many commonly used function spaces. The kernel of the integral operators involves a H\"older dependence in the variables and is not assumed to be translation invariant.
Keywords
Cite
@article{arxiv.2212.01950,
title = {Gradient regularity and first-order potential estimates for a class of nonlocal equations},
author = {Tuomo Kuusi and Simon Nowak and Yannick Sire},
journal= {arXiv preprint arXiv:2212.01950},
year = {2024}
}
Comments
56 pages. To appear in American Journal of Mathematics