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A Variational Approach to Second Order Mean Field Games with Density Constraints: the Stationary Case By ​Prof. Francisco J. Silva (University of Limoges)

  • Class schedule:  Wednesday June 3rd, 2015 from 2:00 to 3:00pm
  • Location: Building 1, Room 4214

Abstract
In this work we study the existence of solutions of a stationary Mean Field Game (MFG) system with a density constraint on the distribution of the agents. We prove the existence of a solution for both, the subquadratic and the superquadratic cases. Our approach is based on the interpretation of the MFG system as the optimality condition of the optimal problem of a stationary Fokker-Planck equation. Using tools from convex analysis and some sharp results in the theory of elliptic equations with measure data, we derive first the optimality system for the qualified problem, i.e. when the Slater condition for the density constraint is satisfied. For non qualified problems, we proceed by using an approximation argument.  

Biography
Francisco J. Silva received his B.Sc. degree in mathematical engineering from the University of Chile and the PhD degree in applied mathematics from Ecole polytechnique. Currently, he is an associated professor at the University of Limoges.  His main research interests are deterministic and stochastic  optimal control theories.