No abstract

In this paper, the value function of a Bolza optimal control problem with state constraints is characterized as the unique lower semicontinuous solution of a Hamilton᎐Jacobi equation. The state constraints are given by an arbitrary closed set with possibly empty interior. In particular, Soner's inward pointing condition is extended here to the case of degenerate state constraints.

In this paper, existence and uniqueness of generalized solutions of some first order Hamilton Jacobi equations are proved. This task is accomplished by showing that the value function for a certain problem of the calculus of variations is the unique solution of the PDE. This can be viewed as a representation formula of the solution.2000 Mathematics Subject Classification. 49J15, 49L25, 49J24, 34A60, 35D05.

No abstract

No abstract