On the existence of stationary solutions of extended mean-field games

by D. Gomes, S. Patrizi, V. Voskanyan
Refereed Journals Year: 2014


D. Gomes, S. Patrizi and V. Voskanyan, On the existence of stationary solutions of extended mean-field games. D. Gomes, S. Patrizi and V. Voskanyan. Nonlinear Analysis: Theory, Methods & Applications, Volume 99, April 2014, Pages 49–79


In this paper we consider extended stationary mean field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean field games in [GPSM12]. In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in [LL06a], [GSM11] or [GPSM12] this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where existence of classical solutions can be proved.




Extended mean field games Stationary mean-field games