Boundary control problems with convex cost and dynamic programming in infinite dimension. II: Existence for HJB
The author studies the Hamilton-Jacobi-Bellman equation originating from boundary control problems for partial differential equations. The state equation of control problems is linear and the cost functional is convex. The author shows that the value function of the control problem is a solution of an integral version of the Hamilton-Jacobi-Bellman equation. She also proves that this solution is the limit of classical solutions of approximating equations, for part I see Zbl 1150.49008.
scientific article; zbMATH DE number 2154997