Fully nonlinear degenerate equations with applications to grad equations

We consider a class of degenerate elliptic fully nonlinear equations with applications to Grad equations:(|Du|?M+?,?D2u(x) = f|u ? u(x)| in ?u = g on ?,where ??1 is a constant, ? is a bounded domain in RN with C1,1 boundary. We prove the existence of a W2,p-viscosity solution to the above equation, which degenerates when the gradient of the solution vanishes.