Boundary Lipschitz regularity and the Hopf lemma on Reifenberg domains for fully nonlinear elliptic equations

In this paper, we prove the boundary Lipschitz regularity and the Hopf Lemma by a unified method on Reifenberg domains for fully nonlinear elliptic equations. Precisely, if the domain Omega satisfies the exterior Reifenberg C-1,C-Dini condition at x(0) is an element of partial derivative Omega (see Definition 1.3), the solution is Lipschitz continuous at x(0); if Omega satisfies the interior Reifenberg C-1,C-Dini condition at x(0) (see Definition 1.4), the Hopf lemma holds at x(0). Our paper extends the results under the usual C-1,C-Dini condition.