Sala Seminari (Dip. Matematica).
In the talk we introduce the so-called mean field planning problem: a coupled system of PDEs, a forward continuity equation and a backward Hamilton-Jacobi equation. The problem can be viewed as a modification of the mean field games system as well as a generalization of the classical optimal transportation problem in its dynamic formulation à la Benamou-Brenier. We concentrate on the variational structure of the problem, from which a notion of weak solution can be given. In particular, we discuss a well-posedness result in a L p -framework, as well as optimality conditions at the level of minimizing paths. The talk is based on a joint work with A. Porretta and G. Savaré. Sito web: https://valep3.wixsite.com/seminarimap