Regularity theory for nonlocal equations with VMO coefficients
Analysis of PDEs
2021-10-26 v2
Abstract
We prove higher regularity for nonlinear nonlocal equations with possibly discontinuous coefficients of VMO-type in fractional Sobolev spaces. While for corresponding local elliptic equations with VMO coefficients it is only possible to obtain higher integrability, in our nonlocal setting we are able to also prove a substantial amount of higher differentiability, so that our result is in some sense of purely nonlocal type. By embedding, we also obtain higher H\"older regularity for such nonlocal equations.
Keywords
Cite
@article{arxiv.2101.11690,
title = {Regularity theory for nonlocal equations with VMO coefficients},
author = {Simon Nowak},
journal= {arXiv preprint arXiv:2101.11690},
year = {2021}
}
Comments
59 pages. To appear in Annales de l'Institut Henri Poincar\'e, Analyse Non Lin\'eaire