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 , D u , D 2 u ) = 0 in Ω to satisfy | u ( x ) − u ( y ) | ⩽ C | x − y | α for some α ∈ ( 0 , 1 ) when x ∈ Ω and y ∈ ∂ Ω .