Free Access
Volume 21, Number 3, July-September 2015
Page(s) 690 - 722
Published online 20 May 2015
  1. L. Ambrosio and G. Crippa, Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields, Transport equations and multi-D hyperbolic conservation laws. Springer (2008) 3–57. [Google Scholar]
  2. P. Cardaliaguet, Long time average of first order mean field games and weak KAM theory. Dyn. Games Appl. 3 (2013) 473–488. [Google Scholar]
  3. P. Cardaliaguet, Weak solutions for first order mean field games with local coupling. Preprint arXiv:1305.7015 (2013). [Google Scholar]
  4. P. Cardaliaguet and L. Silvestre, Hölder continuity to Hamilton−Jacobi equations with superquadratic growth in the gradient and unbounded right-hand side. Comm. Partial Differ. Eq. 37 (2012) 1668–1688. [Google Scholar]
  5. P. Cardaliaguet, G. Carlier, and B. Nazaret, Geodesics for a class of distances in the space of probability measures. Calc. Var. Partial Differ. Eq. (2012) 1–26. [Google Scholar]
  6. P. Cardaliaguet, J.-M. Lasry, P.-Louis Lions and A. Porretta, et al., Long time average of mean field games. Networks and Heterogeneous Media 7 (2012) 279–301. [Google Scholar]
  7. P. Cardaliaguet, J.-Michel Lasry, P.-L. Lions and A. Porretta, Long time average of mean field games with a nonlocal coupling. SIAM J. Control Optim. 51 (2013) 3558–3591. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.-David B. and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375–393. [CrossRef] [MathSciNet] [Google Scholar]
  9. I. Ekeland and R. Temam, Convex analysis and variational problems, vol. 28, SIAM (1976). [Google Scholar]
  10. L.C. Evans, Some new PDE methods for weak KAM theory. Calc. Var. Partial Differ. Eq. 17 (2003) 159–177. [Google Scholar]
  11. D.A. Gomes D.A., J. Mohr, and R.R. Souza, Discrete time, finite state space mean field games. J. Math. Pures Appl. 93 (2010) 308–328. [CrossRef] [MathSciNet] [Google Scholar]
  12. D.A. Gomes, E. Pimentel and H. Sánchez-Morgado, Time dependent mean-field games in the superquadratic case. Preprint arXiv:1311.6684 (2013). [Google Scholar]
  13. D.A. Gomes, E. Pimentel, and H. Sánchez-Morgado, Time dependent mean-field games in the superquadratic case. Commun. Partial Differ. Eq. 40 (2015) 40–76. [Google Scholar]
  14. P.J. Graber, Optimal control of first-order Hamilton−Jacobi equations with linearly bounded Hamiltonian. Appl. Math. Optimization 70 (2014) 185–224. [CrossRef] [Google Scholar]
  15. M. Huang, P.E. Caines and R.P. Malhamé, Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized ε-Nash equilibria. Automatic Control, IEEE Transactions 52 (2007) 1560–1571. [Google Scholar]
  16. M. Huang, R.P. Malhamé and P.E. Caines, Large population stochastic dynamic games: closed-loop McKean−Vlasov systems and the Nash certainty equivalence principle. Comm. Inform. Syst. 6 (2006) 221–252. [Google Scholar]
  17. E. Kosygina and S.R.S. Varadhan, Homogenization of Hamilton−Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium. Comm. Pure Appl. Math. 61 (2008) 816–847. [CrossRef] [MathSciNet] [Google Scholar]
  18. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. i − le cas stationnaire. C. R. Math. 343 (2006) 619–625. [Google Scholar]
  19. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. ii − horizon fini et contrôle optimal. C. R. Math. 343 (2006) 679–684. [Google Scholar]
  20. J.-M. Lasry and P.-L. Lions, Mean field games. Japan. J. Math. 2 (2007) 229–260. [Google Scholar]
  21. P.-L. Lions, Théorie des jeux de champ moyen et applications (mean field games), Cours du College de France. 2009 (2007). [Google Scholar]
  22. A. Porretta, Weak solutions to Fokker-Planck equations and mean field games. Arch. Ration. Mech. Anal. 216 (2015) 1–62. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.