Abstract : 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.
https://hal.archives-ouvertes.fr/hal-00289588
Contributor : Pierre Cardaliaguet <>
Submitted on : Monday, June 23, 2008 - 8:49:02 AM Last modification on : Monday, October 5, 2020 - 11:32:02 AM Long-term archiving on: : Friday, May 28, 2010 - 10:43:10 PM
Pierre Cardaliaguet. A double obstacle problem arising in differential game theory. Journal of Mathematical Analysis and Applications, Elsevier, 2009, 360 (1), pp.95-107. ⟨10.1016/j.jmaa.2009.06.041⟩. ⟨hal-00289588⟩