In this talk, we study a mean field game inspired by crowd motion in which agents evolve in a domain and want to reach its boundary minimizing their travel time. Interactions between agents occur through their dynamic, which depends on the distribution of all agents. First, we provide a Lagrangian formulation for our mean field game and prove existence of equilibria, which are shown to satisfy a MFG system. The main result, which relies on the semi-concavity of the value function of this optimal control problem, states that an L^p initial distribution of agents gives rise to an L^p distribution of agents at each time t>0.
I'm currently a postdoc at University of British Columbia. I obtained my PhD in Fundamental Mathematics from Université Paris-Sud on July 2018. My domain of interest is Optimal Transport, Optimal Control, Mean Field Games, Stochastic Transport and Shape Optimization.