Existence of solutions to the Hamilton-Jacobi-Bellman equation under quadratic growth conditions

Abstract

In this paper we show the existence of solutions with quadratic growth to Hamilton-Jacobi-Bellman equations. We assume that the Hamiltonian has the quadratic growth both in x and p. We obtain the explicit Lipschitz bound of solutions in the weighted sup-norm. Also, we discuss the vanishing viscosity limit of solutions and show the existence of viscosity solutions to the resulting Hamilton Jacobi equation. © 2001 Academic Press.