Preprint

Inserted: 22 aug 2024

Year: 2024

Abstract:

We investigate an infinite dimensional partial differential equation of Isaacs’ type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transportcontinuity equation, where the control is given by the vector velocity field. Our study is set in the framework of the viscosity solutions theory in Hilbert spaces, and we prove the uniqueness of the value functions as solutions of the Isaacs equation.

Keywords: Viscosity solutions, differential games, Mass transportation, infinite-dimensional Isaacs equation, zero-sum games