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|^γ M⁺ (λ,Λ<inf>D</inf>² u(x)⁾ = f⁽ |u ≥ u(x)|⁾ in Ω u = g on ∂Ω, where γ ≥ 1 is a constant, Ω is a bounded domain in R^N with C^1,1 boundary. We prove the existence of a W^2,p-viscosity solution to the above equation, which degenerates when the gradient of the solution vanishes.