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

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.

28 pages. Final version, to appear in Nonlinear Analysis