Interior regularity for fractional systems
Analysis of PDEs
2016-04-18 v1
Abstract
We study the regularity of solutions of elliptic fractional systems of order 2s, , where the right hand side f depends on a nonlocal gradient and has the same scaling properties as the nonlocal operator. Under some structural conditions on the system we prove interior H\"older estimates in the spirit of [1]. Our results are stable in s allowing us to recover the classic results for elliptic systems due to S. Hildebrandt and K. Widman [6] and M. Wiegner [9].
Cite
@article{arxiv.1604.04442,
title = {Interior regularity for fractional systems},
author = {Luis Caffarelli and Gonzalo Davila},
journal= {arXiv preprint arXiv:1604.04442},
year = {2016}
}