RECENT RESULTS ABOUT THE MAXIMUM PRINCIPLE ON UNBOUNDED DOMAINS

I will give an overview of some results concerning the validity of sign propagation property u ≤ 0 on ∂Ω, F(x,u,Du,D2u) ≥ 0 in Ω implies u ≤ 0 in Ω in an unbounded domain Ω satisfying either measure-type or geometric conditions related to the directions of ellipticity of the (possibly) degenerate fully nonlinear mapping F.