Nonlinear nonlocal equations in Reifenberg flat domains

Abstract

We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish several fine boundary regularity results for solutions, and their gradient, near the boundary. To the best of our knowledge, each of our results is new even in the linear case.