Calculus of Variations and Geometric Measure Theory

A variational approach to the mean field planning problem

Carlo Orrieri

created by pagliari on 30 Jan 2018

30 jan 2018 -- 17:00   [open in google calendar]

Aula Seminari, Dip. di Matematica, Univ. Pisa


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.