A double obstacle problem arising in differential game theory

A Hamilton-Jacobi equation involving a double obstacle problem is investigated. The link between this equation and the notion of dual solutions-introduced in IS. As Soulaimani, Infinite horizon differential games with asymmetric information, PhD thesis; R Cardaliaguet, Differential games with asymmetric information, SIAM J. Control Optim. 46 (3) (2007) 816-838; R Cardaliaguet, C. Rainer. Stochastic differential games with asymmetric information, Appl. Math. Optim. 59 (1) (2009) 1-36] 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. (C) 2009 Elsevier Inc. All rights reserved.