Open Access
Volume 29, 2023
Article Number 14
Number of page(s) 21
Published online 15 February 2023
  1. Y. Achdou and A. Porretta, Mean field games with congestion. Ann. I. H. Poincaré Anal. Nonlinéaire 35 (2018) 443–480. [CrossRef] [Google Scholar]
  2. Y. Achdou and A. Porretta, Mean field games modeling crowd congestion, slides presented at “Mean field games and related topics - 5". CIRM, Levico (2019). [Google Scholar]
  3. Y. Achdou and M. Laurière, Mean field type control with congestion. Appl. Math. Optim. 73 (2016) 393–418. [CrossRef] [MathSciNet] [Google Scholar]
  4. S. Bernstein, Sur la généralisation du problème de Dirichlet. (Deuxieme partie). Math. Ann. 69 (1910) 82–136. [CrossRef] [MathSciNet] [Google Scholar]
  5. P.E. Caines, M. Huang and R.P. Malhamé, Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6 (2006) 221–251. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Cardaliaguet, Weak solutions for first order mean field games with local coupling, Analysis and geometry in control theory and its applications. Springer INdAM Ser. 11 (2015) 111–158. [Google Scholar]
  7. P. Cardaliaguet and P.J. Graber, Mean field games systems of first order. ESAIM: COCV 21 (2015) 690–722. [CrossRef] [EDP Sciences] [Google Scholar]
  8. P. Cardaliaguet, P.J. Graber, A. Porretta and D. Tonon, Second order mean field games with degenerate diffusion and local coupling. Nonlinear Differ. Equ. Appl. 22 (2015) 1287–1317. [CrossRef] [Google Scholar]
  9. D. Evangelista, R. Ferreira, D.A. Gomes, L. Nurbekyan and V. Voskanyan, First-order, stationary mean-field games with congestion. Nonlinear Analysis 173 (2018) 37–74. [CrossRef] [MathSciNet] [Google Scholar]
  10. R. Fiorenza, Sui problemi di derivata obliqua per le equazioni ellittiche. Ric. Mat. 8 (1959) 83–110. [Google Scholar]
  11. R. Fiorenza, Sulla hölderianità dalle soluzioni dei problemi de derivata obliqua regolare del secondo ordine. Ric. Mat. 14 (1965) 102–123. [Google Scholar]
  12. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Springer, Berlin (2001). [CrossRef] [Google Scholar]
  13. D. Gomes and V.K. Voskanyan, Short-time existence of solutions for mean-field games with congestion. Journal of the London Mathematical Society 92 (2015) 778–799. [CrossRef] [MathSciNet] [Google Scholar]
  14. D. Gomes, V.K. Voskanyan, Extended deterministic mean-field games. SIAM J. Control Optim. 54 (2016) 1030–1055. [CrossRef] [MathSciNet] [Google Scholar]
  15. P.J. Graber, Weak Solutions for Mean Field Games with Congestion. Preprint arXiv:1503.04733 (2018). [Google Scholar]
  16. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
  17. G.M. Lieberman, The nonlinear oblique derivative problem for quasilinear elliptic equations. Non-linear Anal. Theory, Methods & Appl. 8 (1984). [Google Scholar]
  18. G.M. Lieberman, Solvability of quasilinear elliptic equations with nonlinear boundary conditions. Trans. Am. Math. Soc. 273 (1982) 753–765. [CrossRef] [Google Scholar]
  19. P.-L. Lions, Courses at the Collàege de France. [Google Scholar]
  20. P.-L. Lions and P.E. Souganidis, Extended mean-field games. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020) 611–625. [CrossRef] [Google Scholar]
  21. N. Mimikos-Stamatopoulos and S. Munoz, Regularity and long time behavior of one-dimensional first-order mean field games and the planning problem. Preprint arXiv:2204.06474 (2022). [Google Scholar]
  22. S. Munoz, Classical and weak solutions to local first-order mean field games through elliptic regularity. Ann. I. H. Poincaré Anal. Non Linéaire 39 (2022) 1–39. [CrossRef] [MathSciNet] [Google Scholar]
  23. A. Porretta, Regularizing effects of the entropy functional in optimal transport and planning problems. J. Funct. Anal. 284 (2023). [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.