Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. I. Equations of unbounded and degenerate control problems without uniqueness

Abstract

We prove general optimality principles for semicontinuous viscosity solutions of Hamilton-Jacobi equations. We also characterize the minimal nonnegative supersolution and the maximal subsolution null on a closed given set for a class of equations without uniqueness, including the degenerate eikonal equation and the Bellman equation of the linear quadratic control problem.