A weak comparison principle for solutions of very degenerate elliptic   equations
  We prove a comparison principle for weak solutions of elliptic quasilinear equations in divergence form whose ellipticity constants degenerate at every point where $\nabla u \in K$, where $K\subset \mathbb{R}^N$ is a Borel set containing the origin. 
Giulio Ciraolo
math.AP