Geodesic
Differential games and Hamilton-Jacobi-Isaacs equations in metric spaces
Minimax theory and its applications, Tome 8 (2023) no. 1
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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.
Mots-clés : Hamilton-Jacobi equations, metric space, differential games, viscosity solutions 
@article{MTA_2023_8_1_a5,
     author = {Qing Liu and Xiaodan Zhou},
     title = {Differential games and {Hamilton-Jacobi-Isaacs} equations in metric spaces},
     journal = {Minimax theory and its applications},
     year = {2023},
     volume = {8},
     number = {1},
     zbl = {1516.35421},
     url = {http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a5/}
}
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Qing Liu; Xiaodan Zhou. Differential games and Hamilton-Jacobi-Isaacs equations in metric spaces. Minimax theory and its applications, Tome 8 (2023) no. 1. http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a5/