Comparison principles and Lipschitz regularity for some nonlinear   degenerate elliptic equations
  We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for operators of the form $\nabla^2 \psi + L(x,\psi,\nabla \psi)$ which are non-decreasing in $\psi$. 
YanYan Li, Luc Nguyen, Bo Wang
math.AP math.DG