Title: Sobolev regularity for first order Mean Field Games
Speaker: Jameson Graber (Baylor University)
Date and Time: Monday, March 26, 5:00pm-6:00pm
Place: Monroe 113
Abstract. In their seminal 2007 paper, Lasry and Lions proposed a system of PDE to model games with a continuum of infinitesimal interacting agents. Since then many authors have proved several results on the well-posedness and regularity of solutions, mostly employing techniques from the theory of parabolic PDE. More recently, a satisfactory definition of weak solution has been provided which allows us to study weak solutions of degenerate and first-order systems, for which the question of regularity can no longer be addressed using classical methods. In this talk, based on recent joint work with Alpar Meszaros, I will show how methods from the calculus of variations can be used to prove additional regularity of weak solutions to first-order mean field games. Additionally I will illustrate some connections to other work in optimal transport theory.