Viscosity solutions of Isaacs' equations and differential games with Lipschitz controls

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Abstract

It is demonstrated that the upper and lower values of a two-person, zero-sum differential game solve the respective upper and lower Isaacs' equations in the viscosity sense (introduced by Crandall and Lions (Trans. Amer. Math. Soc. 277 (1983), 1-42). Since such solutions are unique, this yields a fairly simple proof that the game has value should the minimax condition hold. As a further application of viscosity techniques, a new and simpler proof that the upper and lower values can be approximated by the values of certain games with Lipschitz controls is given. © 1984.

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Barron, E. N., Evans, L. C., & Jensen, R. (1984). Viscosity solutions of Isaacs’ equations and differential games with Lipschitz controls. Journal of Differential Equations, 53(2), 213–233. https://doi.org/10.1016/0022-0396(84)90040-8

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