Non-convex Hamilton–Jacobi equations with gradient constraints

We study non-convex Hamilton–Jacobi equations in the presence of gradient constraints and produce new, optimal, regularity results for solutions. A distinctive feature those regards existence a lower bound to norm gradient; it competes with elliptic operator governing problem, affecting This class models relates various important questions finds applications several areas; particular interest is modeling optimal dividends problems multiple insurance companies risk theory singular stochastic control reversible investment models.