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All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 20 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 20
Number of page(s) 47
DOI https://doi.org/10.1051/cocv/2025094
Published online 18 March 2026
  1. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal. C. R. Math. Acad. Sci. Paris 343 (2006) 679–684. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343 (2006) 619–625. [CrossRef] [MathSciNet] [Google Scholar]
  3. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
  4. 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 (2006) 221–251. [Google Scholar]
  5. Y. Achdou, F.J. Buera, J.-M. Lasry, P.-L. Lions and B. Moll, Partial differential equation models in macroeconomics. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 372 (2014) 20130397. [Google Scholar]
  6. P. Cannarsa, R. Capuani and P. Cardaliaguet, Mean field games with state constraints: from mild to pointwise solutions of the PDE system. Calc. Var. Part. Differ. Equ. 60 (2021) Paper No. 108. [Google Scholar]
  7. R. Capuani and A. Marigonda, Constrained mean field games equilibria as fixed point of random lifting of set-valued maps. IFAC-PapersOnLine 55 (2022) 180–185. 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022. [CrossRef] [MathSciNet] [Google Scholar]
  8. R. Capuani, A. Marigonda and M. Ricciardi, Random lift of set valued maps and applications to multiagent dynamics. Set-Valued Var. Anal. 31 (2023) 28. [Google Scholar]
  9. P. Cannarsa, W. Cheng, C. Mendico and K. Wang, Weak KAM approach to first-order mean field games with state constraints. J. Dyn. Differ. Equ. 35 (2023) 1885–1916. [Google Scholar]
  10. A. Porretta and M. Ricciardi, Ergodic problems for second-order mean field games with state constraints. Commun. Pure Appl. Anal. 23 (2024) 620–644. [Google Scholar]
  11. L. Campi and M. Fischer, n-player games and mean field games with absorption. Ann. Appl. Probab. 28 (2018) 2188–2242. [Google Scholar]
  12. D. Gomes, E. Pimentel and H. Sánchez-Morgado, Time-dependent mean-field games in the subquadratic case. Commun. Part. Differ. Equ. 40 (2015) 40–76. [Google Scholar]
  13. D. Gomes, E. Pimentel and H. Sánchez-Morgado, Time-dependent mean-field games in the superquadratic case. ESAIM Control Optim. Calc. Var. 22 (2016) 562–580. [Google Scholar]
  14. A. Porretta, Weak solutions to Fokker-Planck equations and mean field games. Arch. Ration. Mech. Anal. 216 (2015) 1–62. [Google Scholar]
  15. M. Cirant, Multi-population Mean Field Games systems with Neumann boundary conditions. J. Math. Pures Appl. 103 (2015) 1294–1315. [Google Scholar]
  16. A. Festa, S. Gottlich and M. Ricciardi, Forward-forward mean field games in mathematical modeling with application to opinion formation and voting models. Dyn. Games Appl. 15 (2024) 664–692. [Google Scholar]
  17. L. Di Persio, M. Garbelli and M. Ricciardi, The master equation in a bounded domain with absorption. preprint on arXiv, arXiv:2203.15583 (2023). [Google Scholar]
  18. M. Ricciardi, The master equation in a bounded domain with Neumann conditions. Commun. Part. Differ. Equ. 47 (2022) 912–947. [Google Scholar]
  19. M. Ricciardi, The convergence problem in mean field games with Neumann boundary conditions. SIAM J. Math. Anal. 55 (2023) 3316–3343. [Google Scholar]
  20. A. Porretta and M. Ricciardi, Mean field games under invariance conditions for the state space. Commun. Part. Diff. Equ. 45 (2020) 146–190. [Google Scholar]
  21. P. Cardaliaguet, Weak solutions for first order mean field games with local coupling. Springer INdAM Ser. 11 (2013) 05. [Google Scholar]
  22. P. Cardaliaguet and P. Graber, Mean field games systems of first order. ESAIM Control Optim. Calc. Var. 21 (2014) 01. [Google Scholar]
  23. M. Alharbi, A.Y. Ashrafyan and D. Gomes, A first-order mean-field game on a bounded domain with mixed boundary conditions. Preprint arXiv: arXiv:2305.15952v3 (2023). [Google Scholar]
  24. L.C. Evans and D. Gomes, Linear programming interpretations of Mather's variational principle. ESAIM Control Optim. Calc. Var. 8 (2002) 693–702. A tribute to J.L. Lions. [Google Scholar]
  25. D. Gomes and E. Valdinoci, Duality theory, representation formulas and uniqueness results for viscosity solutions of Hamilton-Jacobi equations, in Dynamics, games and science. II, vol. 2 of Springer Proc. Math.. Springer, Heidelberg (2011) 361–386. [Google Scholar]
  26. D. Gomes and E. Valdinoci, Entropy penalization methods for Hamilton-Jacobi equations. Adv. Math. 215 (2007) 94–152. [Google Scholar]
  27. D.A. Gomes, H. Mitake and H.V. Tran, The large time profile for Hamilton—Jacobi—Bellman equations. Mathematische Annalen 384 (2022) 1409–1459. [Google Scholar]
  28. P.J. Graber, Optimal control of first-order Hamilton-Jacobi equations with linearly bounded Hamiltonian. Appl. Math. Optim. 70 (2014) 185–224. [Google Scholar]
  29. P.J. Graber, A.R. Mészáros, F.J. Silva and D. Tonon, The planning problem in mean field games as regularized mass transport. Calc. Var. Partial Differ. Equ. 58 (2019) 115. [Google Scholar]
  30. I. Ekeland and R. Témam, Convex Analysis and Variational Problems. Society for Industrial and Applied Mathematics (1999). [Google Scholar]
  31. A. Porretta, On the weak theory for mean field games systems. Boll. Unione Mat. Ital. 10 (2017) 411–439. [Google Scholar]
  32. M.C. Delfour and J.P. Zolesio, Shape analysis via oriented distance functions. J. Funct. Anal. 123 (1994) 129–201. [Google Scholar]
  33. M. Bardi, A. Cesaroni and L. Rossi, Nonexistence of nonconstant solutions of some degenerate bellman equations and applications to stochastic control. ESAIM Control Optim. Calc. Var. 22 (2016) 842–861. cvgmt preprint. [Google Scholar]
  34. P. Cannarsa, G. Da Prato and H. Frankowska, Invariant measures associated to degenerate elliptic operators. Indiana Univ. Math. J. 59 (2010) 53–78. [Google Scholar]
  35. D. Castorina, A. Cesaroni and L. Rossi, On a parabolic Hamilton-Jacobi-Bellman equation degenerating at the boundary. Commun. Pure Appl. Anal. 15 (2016) 1251–1263. [Google Scholar]
  36. P. Cardaliaguet, P. Graber, A. Porretta and D. Tonon, Second order mean field games with degenerate diffusion and local coupling. NoDEA Nonlinear Differ. Equ. Appl. 22 (2015) 1287–1317. [Google Scholar]
  37. H. Sohr, The Navier-Stokes Equations: An Elementary Functional Analytic Approach. Birkhäuser Advanced Texts Basler Lehrbücher (2001). [Google Scholar]
  38. J. Simon, Compact sets in the space lp(0,t; b). Ann. Mat. Pura Appl. 146 (1986) 65–96. [Google Scholar]

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