Boundary regularity for viscosity solutions to degenerate elliptic PDEs

Sufficient conditions are given for the solutions to the (fully nonlinear, degenerate) elliptic equation F(x,u,Du,D2u)=0 in Ω to satisfy |u(x)−u(y)|⩽Cα|x−y| for some α∈(0,1) when x∈Ω and y∈∂Ω.