Boundary Hölder regularity for the fractional Laplacian over Reifenberg flat domains via ABP maximum principle

For $0<s<1$, we consider the nonlocal equation $(-\mathrm{\Delta }{)}^{s}u=f$ over a Reifenberg flat domain $\mathrm{\Omega }$ with $f\in C(\bar{\mathrm{\Omega }})$ and null Dirichlet exterior condition. Given $\alpha \in (0,s)$, we prove that weak solutions are $\alpha$-Hölder continuous up to the boundary when the flatness parameter is small enough. The main ingredients of the proof are an iterative argument and a nonlocal version of the ABP maximum principle.