Nonsmooth semipermeable Barriers, Isaacs' equation, and application to a differential game with one target and two players
The author discusses barriers of a differential game. In this context, two players act on a dynamic system through two controls, the first trying to reach a target given in advance and the second trying to avoid this. Since the pioneering work of Isaacs it is well-known that if the boundary of the victory domain of one of the players is regular (a \(C^2\)-manifold for instance) this boundary has some semipermeability property and is the solution of some PDE. In this paper, a complete extension of this phenomenon to victory domains whose boundary are only the boundary of a closed set is presented. This approach allows to express the barriers as generalized solution of suitable PDE. This paper in some sense solves a problem unsolved since the beginning of the theory of differential games.
scientific article; zbMATH DE number 1057312
scientific article