L. Ambrosio, N. Gigli, and G. Savarè, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, 2008.

J. D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numerische Mathematik, vol.84, issue.3, pp.375-393, 2000.
DOI : 10.1007/s002110050002

R. Carmona and F. Delarue, Probabilist analysis of Mean-Field Games, 2013.

P. Cardaliaguet, Weak Solutions for First Order Mean Field Games with Local Coupling
DOI : 10.1007/978-3-319-06917-3_5

URL : https://hal.archives-ouvertes.fr/hal-00827957

P. Cardaliaguet and P. J. Graber, Mean field games systems of first order, ESAIM: Control, Optimisation and Calculus of Variations, vol.21, issue.3
DOI : 10.1051/cocv/2014044

URL : https://hal.archives-ouvertes.fr/hal-00925905

P. Cardaliaguet, G. Carlier, and B. Nazaret, Geodesics for a class of distances in the space of probability measures, Calculus of Variations and Partial Differential Equations, vol.39, issue.1, pp.2012-2013
DOI : 10.1007/s00526-012-0555-7

URL : https://hal.archives-ouvertes.fr/hal-00686908

P. Cardaliaguet and L. Silvestre, H??lder Continuity to Hamilton-Jacobi Equations with Superquadratic Growth in the Gradient and Unbounded Right-hand Side, Communications in Partial Differential Equations, vol.38, issue.1, pp.1668-1688, 2012.
DOI : 10.4171/RMI/80

P. Cardaliaguet, J. Lasry, P. Lions, and A. Porretta, Long time average of mean field games, Networks and Heterogeneous Media, vol.7, issue.2, pp.279-301, 2012.
DOI : 10.3934/nhm.2012.7.279

URL : https://hal.archives-ouvertes.fr/hal-00767403

E. Dibenedetto, Degenerate parabolic equations, 1993.
DOI : 10.1007/978-1-4612-0895-2

R. Diperna and P. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Inventiones mathematicae, pp.98-511, 1989.

I. Ekeland, T. , and R. , Convex analysis and variational problems, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.28, 1999.
DOI : 10.1137/1.9781611971088

D. A. Gomes and E. Pimentel, Sánchez-Morgado, H. Time dependent mean-field games in the subquadratic case. arXiv preprint arXiv:1311, 2013.

D. A. Gomes and E. Pimentel, Sánchez-Morgado, H. Time dependent mean-field games in the superquadratic case. arXiv preprint arXiv:1311, 2013.

P. J. Graber, Optimal Control of First-Order Hamilton???Jacobi Equations with Linearly Bounded Hamiltonian, Applied Mathematics & Optimization, vol.9, issue.6, pp.1-40, 2014.
DOI : 10.1007/s00245-014-9239-3

URL : https://hal.archives-ouvertes.fr/hal-00871964

M. Huang, R. P. Malhamé, and P. E. Caines, Large population stochastic dynamic games: closedloop McKean-Vlasov systems and the Nash certainty equivalence principle. Communication in information and systems, pp.221-252, 2006.

H. Ishii, On the equivalence of two notions of weak solutions, viscosity solutions and distribution solutions, Funkcial. Ekvac, vol.38, issue.1, pp.101-120, 1995.

J. Lasry and P. Lions, Jeux ?? champ moyen. I ??? Le cas stationnaire, Comptes Rendus Mathematique, vol.343, issue.9, pp.619-625, 2006.
DOI : 10.1016/j.crma.2006.09.019

J. Lasry and P. Lions, Jeux ?? champ moyen. II ??? Horizon fini et contr??le optimal, Comptes Rendus Mathematique, vol.343, issue.10, pp.679-684, 2006.
DOI : 10.1016/j.crma.2006.09.018

J. Lasry and P. Lions, Mean field games, Japanese Journal of Mathematics, vol.4, issue.1, pp.229-260, 2007.
DOI : 10.1007/s11537-007-0657-8

URL : https://hal.archives-ouvertes.fr/hal-00667356

L. Bris, C. Lions, and P. , Existence and Uniqueness of Solutions to Fokker???Planck Type Equations with Irregular Coefficients, Communications in Partial Differential Equations, vol.83, issue.7, pp.1272-1317, 2008.
DOI : 10.1214/aop/1176995608

URL : https://hal.archives-ouvertes.fr/hal-00667315

A. Porretta, Weak Solutions to Fokker???Planck Equations and Mean Field Games, Archive for Rational Mechanics and Analysis, vol.146, issue.4, 2013.
DOI : 10.1007/s00205-014-0799-9

G. Stampacchia, Le probl??me de Dirichlet pour les ??quations elliptiques du second ordre ?? coefficients discontinus, Annales de l???institut Fourier, vol.15, issue.1, pp.189-258, 1965.
DOI : 10.5802/aif.204

. Ceremade, 75775 Paris cedex 16 -France E-mail address: cardaliaguet@ceremade.dauphine.fr 828, Boulevard des Maréchaux, 91762 Palaiseau Cedex E-mail address: jameson.graber@ensta-paristech.fr Dipartimento di Matematica, Via della Ricerca Scientifica 1, 00133 Roma (Italy) E-mail address: porretta@mat.uniroma2.it Ceremade