On the propagation of singularities of semi-convex functions

Abstract: "The paper deals with the propagation of singularities of semi-convex functions. We obtain lower bounds on the degree of the singularities and on the size of the singular set in a neighborhood of a singular point. These results apply to viscosity solutions of Hamilton-Jacobi-Bellman equations. In particular, they provide sufficient conditions for the propagation of singularities, depending only on the geometry of the superdifferential at the singular point."