Caltech/UCLA Joint Analysis Seminar
The planning problem, as introduced by P.-L. Lions, is a model for Nash games with a continuum of players in which the initial and final distributions of states are prescribed. In the first-order case, we have a clear analogy with optimal transport problems, which is reminiscent of the Benamou-Brenier formulation of the Monge-Kantorovitch problem. In this presentation we will give conditions under which existence of solutions is guaranteed for any absolutely continuous initial/final measures. Additionally, we will show how, unlike for classical optimal transport problems, the running costs imposed on the density variable result in extra regularity in both time and space.