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

Simon Nowak

Published 2019-06-14Version 1

In this paper, we study the regularity of weak solutions to a class of nonlocal elliptic equations in Bessel potential spaces $H^{s,p}$ under very mild assumptions on the data. 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 with BMO coefficients to the nonlocal setting.