A Class of Hamilton—Jacobi Equations with Unbounded Coefficients in Hilbert Spaces

We establish existence and comparison theorems for a class of Hamilton—Jacobi equations. The class of Hamilton—Jacobi equations includes and is broader than those studied in [8] We apply the existence and uniqueness results to characterizing the value functions associated with the optimal control of systems governed by partial differential equations of parabolic type. Accepted 11 May 2001. Online publication 5 October 2001.