Moduli of Continuity for Viscosity Solutions

In this paper, we investigate the moduli of continuity for viscosity solutions of a wide class of nonsingular quasilinear evolution equations and also for the level set mean curvature flow, which is an example of singular degenerate equations. We prove that the modulus of continuity is a viscosity subsolution of some one dimensional equation. This work extends B. Andrews’ recent result on moduli of continuity for smooth spatially periodic solutions.