Advanced search
Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 89, 2017 - Issue 6-7: Proceedings of the Hammamet Conference, 19-23 October 2015
Submit an article Journal homepage
91
Views
1
CrossRef citations to date
0
Altmetric
Articles

Global-in-time regularity via duality for congestion-penalized Mean Field Games

Adam ProsinskiEPSRC CDT in Partial Differential Equations, University of Oxford, Oxford, United Kingdom.View further author information
&
Filippo SantambrogioLaboratoire de Mathématiques d’Orsay, University of Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France.Correspondence[email protected]
View further author information
Pages 923-942 | Received 28 Apr 2016, Accepted 12 Jan 2017, Published online: 13 Feb 2017

References

  • L. Ambrosio and A. Figalli, On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations, Calculus Variations Partial Differ. Equ. 31(4) (2008), pp. 497–509.
  • L. Ambrosio and A. Figalli, Geodesics in the space of measure-preserving maps and plans, Arch. Ration. Mech. Anal. 194 (2009), pp. 421–462.
  • L. Ambrosio, N. Gigli, and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures, Lectures in Mathematics, ETH Zürich, Basel, 2005.
  • J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge--Kantorovich mass transfer problem, Numer. Math. 84 (2000), pp. 375–393.
  • J.-D. Benamou and G. Carlier, Augmented Lagrangian methods for transport optimization, mean field games and degenerate elliptic equations, J. Opt. Theor. Appl. 167(1) (2015), pp. 1–26.
  • J.-D. Benamou, G. Carlier, and F. Santambrogio, Variational mean field games, Modelling and Simulation in Science Engineering and Technology, in Active Particles, Volume 1: Theory, Models, ApplicationsN. Bellomo, P. Degond, and E. Tadmor, eds., Birkhauser-Springer, Boston, 2017. doi:10.1007/978-3-319-49996-3.
  • Y. Brenier, Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations, Commun. Pure Appl. Math. 52(4) (1999), pp. 411–452.
  • G. Buttazzo, C. Jimenez, and E. Oudet, An optimization problem for mass transportation with congested dynamics, SIAM J. Control Optim. 48 (2010), pp. 1961–1976.
  • P. Cardaliaguet, Notes on Mean Field Games, Available at https://www.ceremade.dauphine.fr/\~cardalia/MFG20130420.pdf.
  • P. Cardaliaguet, Weak solutions for first order mean field games with local coupling, Springer INdAM Series Vol. 11, in Analysis and Geometry in Control Theory and its Applications, Springer, Basel, 2015, pp. 111–158.
  • P. Cardaliaguet, F. Delarue, J.-M. Lasry, and P.-L. Lions The master equation and the convergence problem in mean field games, preprint (2015). Available at http://arxiv.org/abs/1509.02505.
  • P. Cardaliaguet and P.J. Graber, Mean field games systems of first order, ESAIM: Control Opt. Calculus Variations. 21(3) (2015), pp. 690–722.
  • P. Cardaliaguet, A.R. Mészáros, and F. Santambrogio, First order mean field games with density constraints: Pressure equals price, SIAM J. Control Opt. preprint. 54(5) (2016), pp. 2672–2709.
  • N. Gigli, On the differential structure of metric measure spaces and applications, Memoirs Am. Math. Soc. 236(1113) (2015).
  • O. Guéant, J.-M. Lasry, and P.-L. Lions, Mean field games and applications, in Paris-Princeton Lectures on Mathematical Finance 2010, Springer, Basel, 2011, pp. 205–266.
  • 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, Commun. Inf. Syst. 6(3) (2006), pp. 221–252.
  • J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci. Paris. 343(9) (2006), pp. 619–625.
  • J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal, C. R. Math. Acad. Sci. Paris. 343(10) (2006), pp. 679–684.
  • J.-M. Lasry and P.-L. Lions, Mean field games, Jpn. J. Math. 2(1) (2007), pp. 229–260.
  • P.-L. Lions, Cours au Collège de France. Available at http://www.college-de-france.fr.
  • F. Santambrogio, Optimal Transport for Applied Mathematicians, in Progress in Nonlinear Differential Equations and Their Applications Vol. 87, Birkhäuser, Basel, 2015.
  • F. Santambrogio, Regularity via duality in calculus of variations and degenerate elliptic PDEs, J. Math. Anal. Appl. preprint (2016). Available at http://dx.doi.org/10.1016/j.jmaa.2017.01.030.
  • C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics, AMS, Providence, 2003.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Supercharge Your Next Research Paper: Research and write your next paper with Jenni AI.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.