Upper semi-continuous functions which have sub-level convex sets are close cousins to and contain the convex functions.  Such functions are also called quasi-convex (e.g., http://en.wikipedia.org/wiki/Quasiconvex_function), but this term also can refer to functions which give rise to functionals that are weakly lower semi-continuous.  In this talk I will investigate the connection between sub-level set convex functions and a nonlinear, degenerate elliptic PDE.  I will describe properties of solutions of this PDE, including existence, uniqueness, and regularity.  The context for this work is in the Crandall-Lions theory of viscosity solutions.