A double obstacle problem arising in differential game theory

Pierre Cardaliaguet (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

A Hamilton-Jacobi equation involving a double obstacle problem is investigated. The link between this equation and the notion of dual solutions---recently introduced in the framework of differential games with lack of information---is established. As an application we characterize the convex hull of a function in the simplex as the unique solution of some nonlinear obstacle problem.

Mots clés: Viscosity solutions of Hamilton-Jacobi equations; differential games; convex hull

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet. A double obstacle problem arising in differential game theory. Journal of Mathematical Analysis and Applications, 2009, 360 (1), pp.95-107. ⟨10.1016/j.jmaa.2009.06.041⟩. ⟨hal-00289588⟩