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

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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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     author = {Yu. V. Averboukh},
     title = {Differential games with a~given value function},
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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/