Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. II: Concave operators

We describe the set of propagation of maxima of upper semicontinuous viscosity subsolutions of fully nonlinear, degenerate elliptic Hamilton-Jacobi-Bellman equations in the concave case, i.e., for operators represented as the minimum of a parametrized family of 2(nd) order linear operators. We show that the set where an interior maximum propagates contains the reachable set of a suitable deterministic differential game, as well as the unavoidable set of a controlled diffusion process. We also obtain a Strong Maximum Principle for a class of operators that are not strictly elliptic.