A generalization of the Hamilton-Jacobi equation

After a brief review of the relevant classical theory and a presentation of the concept of generalized gradients, it is demonstrated that, in analogy with the classical case, a locally lipschitz value function satisfies a generalized version of the Hamilton-Jacobi equation. A sufficiency condition for optimality is developed and some examples illustrating various aspects of the generalized theory are presented.Science, Faculty ofMathematics, Department ofGraduat