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Nonsmooth semipermeable barriers, Isaacs’ equation, and application to a differential game with one target and two players

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Abstract

We study the target problem which is a differential game where one of the players aims at reaching a target while the other player aims at avoiding this target forever. We characterize the victory domains of the players by means of geometric conditions and prove that the boundary of the victory domains is a nonsmooth semipermeable surface, i.e., is a solution (in a weak sense) of the Isaacs equation: sup u inf v 〈f (x, u, v),p〉 = 0, wheref is the dynamic of the system,u andv are the respective controls of the players, andp is a normal to the boundary of the victory domains at the pointx.

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  1. CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris cedex 16, France

    P. Cardaliaguet

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  1. P. Cardaliaguet
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Cardaliaguet, P. Nonsmooth semipermeable barriers, Isaacs’ equation, and application to a differential game with one target and two players. Appl Math Optim 36, 125–146 (1997). https://doi.org/10.1007/BF02683340

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