Weak KAM theory for potential MFG

Journal of Differential Equations

Volumn 268, Issue 7, 2020, Pages 3255-3298

  Cardaliaguet, Pierre ^a   Masoero, Marco ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85072770785     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2019.09.060     Document Type: Article

References (34)

1. Aubin, Thierry, Some Nonlinear Problems in Riemannian Geometry. 2013, Springer Science & Business Media.
2. Bogachev, V.I., Krylov, N.V., Röckner, M., Shaposhnikov, S.V., Fokker-Planck-Kolmogorov Equations, Vol. 207. 2015, American Mathematical Soc.
3. Briani, Ariela, Cardaliaguet, Pierre, Stable solutions in potential mean field game systems. Nonlinear Differ. Equ. Appl., 25(1), 2018, 1.
4. Cardaliaguet, P., Notes on Mean Field Games. Technical report, 2010.
5. Cardaliaguet, P., Long time average of first order mean field games and weak kam theory. Dyn. Games Appl. 3:4 (2013), 473–488.
6. Cardaliaguet, P., François, D., Lasry, J.-M., Lions, P.-L., The master equation and the convergence problem in mean field games. arXiv preprint arXiv:1509.02505, 2015.
7. Cardaliaguet, P., Graber, P.J., Porretta, A., Tonon, D., Second order mean field games with degenerate diffusion and local coupling. Nonlinear Differ. Equ. Appl. 22:5 (2015), 1287–1317.
8. Cardaliaguet, P., Lasry, J.-M., Lions, P.-L., Porretta, A., Long time average of mean field games with a nonlocal coupling. SIAM J. Control Optim. 51:5 (2013), 3558–3591.
9. Cardaliaguet, P., Lasry, J.-M., Lions, P.-L., Porretta, A., et al. Long time average of mean field games. Netw. Heterog. Media 7:2 (2012), 279–301.
10. Carmona, René, Delarue, François, Probabilistic Theory of Mean Field Games with Applications I-II. 2018, Springer.
11. Cirant, M., Nurbekyan, L., The variational structure and time-periodic solutions for mean-field games systems. arXiv preprint arXiv:1804.08943, 2018.
12. Cirant, Marco, On the existence of oscillating solutions in non-monotone mean-field games. J. Differ. Equ., 2019.
13. Fathi, A., Solutions kam faibles conjuguées et barrieres de peierls. C. R. Acad. Sci., Ser. 1 Math. 325:6 (1997), 649–652.
14. Fathi, A., Théoreme kam faible et théorie de mather sur les systemes lagrangiens. C. R. Acad. Sci., Ser. 1 Math. 324:9 (1997), 1043–1046.
15. Fathi, A., Sur la convergence du semi-groupe de Lax-Oleinik. C. R. Acad. Sci., Ser. 1 Math. 327:3 (1998), 267–270.
16. Fathi, A., Weak KAM Theorem in Lagrangian Dynamics Preliminary Version Number 10. 2008, CUP.
17. Fathi, Albert, Weak kam theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation. Proceedings of the International Congress of Mathematicians, vol. 3, 2014, 597–621.
18. Ferreira, Rita, Gomes, Diogo A., On the convergence of finite state mean-field games through γ-convergence. J. Math. Anal. Appl. 418:1 (2014), 211–230.
19. Gangbo, Wilfrid, Tudorascu, Adrian, Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem. Adv. Math. 224:1 (2010), 260–292.
20. Gangbo, Wilfrid, Tudorascu, Adrian, Weak kam theory on the Wasserstein torus with multidimensional underlying space. Commun. Pure Appl. Math. 67:3 (2014), 408–463.
21. Gomes, Diogo, Nurbekyan, Levon, On the minimizers of calculus of variations problems in Hilbert spaces. Calc. Var. Partial Differ. Equ. 52:1–2 (2015), 65–93.
22. Gomes, Diogo, Nurbekyan, Levon, An infinite-dimensional weak kam theory via random variables. Discrete Contin. Dyn. Syst. A 36:11 (2016), 6167–6185.
23. Gomes, Diogo, Sedjro, Marc, One-dimensional, forward-forward mean-field games with congestion. Discrete Contin. Dyn. Syst., Ser. B, 11, 2017, 901.
24. Diogo, A., Gomes, Mohr, Joana, Souza, Rafael Rigao, Discrete time, finite state space mean field games. J. Math. Pures Appl. 93:3 (2010), 308–328.
25. Guéant, Olivier, Lasry, Jean-Michel, Lions, Pierre-Louis, Mean field games and applications. Paris-Princeton Lectures on Mathematical Finance 2010, 2011, Springer, 205–266.
26. Huang, M., Malhamé, R.P., Caines, P.E., et al. Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6:3 (2006), 221–252.
27. Lacker, Daniel, Limit theory for controlled McKean–Vlasov dynamics. SIAM J. Control Optim. 55:3 (2017), 1641–1672.
28. Ladyzhenskaia, O.A., Solonnikov, V.A., Ural'tseva, N.N., Linear and Quasi-Linear Equations of Parabolic Type, vol. 23. 1988, American Mathematical Soc.
29. Lasry, J.-M., Lions, P.-L., Jeux à champ moyen. I–Le cas stationnaire. C. R. Math. 343:9 (2006), 619–625.
30. Lasry, J.-M., Lions, P.-L., Jeux à champ moyen. II–horizon fini et contrôle optimal. C. R. Math. 343:10 (2006), 679–684.
31. P.-L. Lions, Mean-field games, Cours au Collège de France (2007–2008).
32. Lions, Pierre-Louis, Souganidis, Panagiotis E., Homogenization of degenerate second-order pde in periodic and almost periodic environments and applications. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 22 (2005), 667–677.
33. Masoero, Marco, On the long time convergence of potential mfg. Nonlinear Differ. Equ. Appl., 26(2), 2019, 15.
34. Mészáros, A.R., Silva, F.J., On the variational formulation of some stationary second-order mean field games systems. SIAM J. Math. Anal. 50:1 (2018), 1255–1277.