$H^{s,p}$ regularity theory for a class of nonlocal elliptic equations

Simon Nowak

$H^{s,p}$ regularity theory for a class of nonlocal elliptic equations

Analysis of PDEs 2019-12-23 v3

Authors: Simon Nowak

Abstract

In this paper, we study the regularity of weak solutions to a class of nonlocal elliptic equations in Bessel potential spaces $H^{s,p}$ . Our main results can be seen as an extension of the well-known $W^{1,p}$ regularity theory for local second-order elliptic equations in divergence form to the nonlocal setting.

Keywords

nonlocal elliptic equations regularity theory weak solutions Bessel potential spaces H^{s,p}

Cite

@article{arxiv.1906.06190,
  title  = {$H^{s,p}$ regularity theory for a class of nonlocal elliptic equations},
  author = {Simon Nowak},
  journal= {arXiv preprint arXiv:1906.06190},
  year   = {2019}
}

Comments

28 pages. Final version, to appear in Nonlinear Analysis

Related papers

View all related →