Existence of Value and Saddle Point in Infinite-Dimensional Differential Games.

We study two-player zero-sum differential games of finite duration in a Hilbert space. Following the Berkovitz notion of strategies, we prove the existence of value and saddle-point equilibrium. We characterize the value as the unique viscosity solution of the associated Hamilton-Jacobi-Isaacs equation using dynamic programming inequalities. [ABSTRACT FROM AUTHOR]