Minimax Theory and its Applications 08 (2023), No. 1, 121--138
Copyright Heldermann Verlag 2023
Differential Games and Hamilton-Jacobi-Isaacs Equations in Metric Spaces
Qing Liu
Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan
qing.liu@oist.jp
Xiaodan Zhou
Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan
xiaodan.zhou@oist.jp
This paper is concerned with a game-based interpretation of Hamilton-Jacobi-Isaacs equations in metric spaces. We construct a two-person continuous-time game in a geodesic space and show that the value function, defined by an explicit representation formula, is the unique solution of the Hamilton-Jacobi equation. Our result develops, in a general geometric setting, the classical connection between differential games and the viscosity solutions to possibly nonconvex Hamilton-Jacobi equations.
Keywords: Hamilton-Jacobi equations, metric space, differential games, viscosity solutions.
MSC: 35Q91, 35R15, 49L25.
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