Geodesic
Differential games with a given value function
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 15-29 Cet article a éte moissonné depuis la source Math-Net.Ru

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The set of solutions of a differential game with a terminal payoff functional is investigated. A method is obtained that allows to establish whether a given function is a value of some differential game with a terminal payoff functional. The condition obtained is in fact a condition for the given function to be a minimax (viscosity) solution of some Hamilton–Jacobi equation with Hamiltonian homogeneous in the third variable. We also obtain a sufficient condition for a function to belong to the set of values of differential games with a terminal payoff function.
Keywords: differential games, minimax solutions of Hamilton-–Jacobi equations. 
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Yu. V. Averboukh. Differential games with a given value function. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 15-29. http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a1/

[1] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR | Zbl

[2] Subbotin A. I., Obobschennye resheniya differentsialnykh uravnenii 1-go poryadka. Perspektivy dinamicheskoi optimizatsii, RKhD, Izhevsk, 2003, 336 pp.

[3] Bardi M., Capuzzo-Dolcetta I., Optimal control and viscosity solutions of Hamilton–Jacobi–Bellman equations, Birkhäuser, Boston, 1997, 570 pp. | MR | Zbl

[4] Demyanov V. F., Rubinov A. M., Osnovy negladkogo analiza i kvazidifferentsialnoe ischislenie, Nauka, M., 1990, 431 pp. | MR

[5] Evans L. K., Gariepi R. F., Teoriya mery i tonkie svoistva funktsii, Nauchnaya kniga, Novosibirsk, 2002, 216 pp.

[6] McShane E. J., “Extension of range of function”, Bull. Amer. Math. Soc., 40:12 (1934), 837–842 | DOI | MR

[7] Evans L. C., Souganidis P. E., “Differential games and representation formulas for solutions of Hamilton–Jacobi–Isaacs equations”, Ind. Univ. Math. J., 33:5 (1984), 773–797 | DOI | MR