Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations

We prove a Strong Maximum Principle for upper semicontinuous viscosity subsolutions to fully nonlinear degenerate parabolic pde's. We also describe the set of propagation of maxima in the case of second order Hamilton-Jacobi-Bellman equations which are either convex or concave with respect to the (u,Du,D² u) variables and we derive the Strong Maximum Principle in some cases, including a class of nonlinear operators which are not strictly parabolic.