Resumen
Abstract We study a class of infinite horizon and exit-time control problems for nonlinear systems with unbounded data using the dynamic programming approach. We prove local optimality principles for viscosity super- and subsolutions of degenerate Hamilton–Jacobi equations in a very general setting. We apply these results to characterize the (possibly multiple) discontinuous solutions of Dirichlet and free boundary value problems as suitable value functions for the above-mentioned control problems. Viscosity solutions - Uniqueness and characterization - Unbounded control problems - Impulsive controls