Semicontinuous Solutions for Hamilton-Jacobi Equations and the L~∞-Control Problem

摘要

We prove uniqueness for extended real-valued lower semicontinuous viscosity solutions of the Bellman equation for L~∞ -control problems. This result is then used to prove uniqueness for lsc solutions of Hamilton--Jacobi equations of the form -u_t+H(t,x,u,-Du)=0, where H(t,x,r,p) is convex in p. The remaining assumptions on