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Volumn 103, Issue 5, 2015, Pages 1294-1315

Multi-population Mean Field games systems with Neumann boundary conditions

Author keywords

Ergodic stochastic control; Mean field games; Multi population models

Indexed keywords


EID: 84926524427     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2014.10.013     Document Type: Article
Times cited : (102)

References (25)
  • 1
    • 84883178689 scopus 로고    scopus 로고
    • Finite difference methods for mean field games
    • Springer, Berlin, Heidelberg, Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications
    • Achdou Y. Finite difference methods for mean field games. Lecture Notes in Mathematics 2013, 1-47. Springer, Berlin, Heidelberg.
    • (2013) Lecture Notes in Mathematics , pp. 1-47
    • Achdou, Y.1
  • 2
  • 4
    • 0033247049 scopus 로고    scopus 로고
    • On the strong maximum principle for fully nonlinear degenerate elliptic equations
    • Bardi M., Da Lio F. On the strong maximum principle for fully nonlinear degenerate elliptic equations. Arch. Math. (Basel) 1999, 73(4):276-285.
    • (1999) Arch. Math. (Basel) , vol.73 , Issue.4 , pp. 276-285
    • Bardi, M.1    Da Lio, F.2
  • 5
    • 24944480311 scopus 로고    scopus 로고
    • On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions
    • Barles G., Da Lio F. On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 2005, 22(5):521-541.
    • (2005) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.22 , Issue.5 , pp. 521-541
    • Barles, G.1    Da Lio, F.2
  • 10
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • Crandall M.G., Ishii H., Lions P.-L. User's guide to viscosity solutions of second order partial differential equations. Bull., New Ser., Am. Math. Soc. 1992, 27(1):1-67.
    • (1992) Bull., New Ser., Am. Math. Soc. , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 11
    • 84887513526 scopus 로고    scopus 로고
    • The derivation of ergodic mean field game equations for several populations of players
    • Feleqi E. The derivation of ergodic mean field game equations for several populations of players. Dyn. Games Appl. 2013, 3(4):523-536.
    • (2013) Dyn. Games Appl. , vol.3 , Issue.4 , pp. 523-536
    • Feleqi, E.1
  • 12
    • 0041625080 scopus 로고    scopus 로고
    • Elliptic Partial Differential Equations of Second Order
    • Springer-Verlag
    • Gilbarg D., Trudinger N.S. Elliptic Partial Differential Equations of Second Order. Classics in Mathematics 2001, Springer-Verlag. 3rd ed.
    • (2001) Classics in Mathematics
    • Gilbarg, D.1    Trudinger, N.S.2
  • 13
    • 84892860445 scopus 로고    scopus 로고
    • On the existence of classical solutions for stationary extended mean field games
    • Gomes D.A., Patrizi S., Voskanyan V. On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal. 2014, 99:49-79.
    • (2014) Nonlinear Anal. , vol.99 , pp. 49-79
    • Gomes, D.A.1    Patrizi, S.2    Voskanyan, V.3
  • 15
    • 79952140932 scopus 로고    scopus 로고
    • Large-population LQG games involving a major player: the Nash certainty equivalence principle
    • Huang M. Large-population LQG games involving a major player: the Nash certainty equivalence principle. SIAM J. Control Optim. 2009/10, 48(5):3318-3353.
    • (2009) SIAM J. Control Optim. , vol.48 , Issue.5 , pp. 3318-3353
    • Huang, M.1
  • 16
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
    • Huang M., Malhamé R.P., Caines P.E. Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 2006, 6(3):221-251.
    • (2006) Commun. Inf. Syst. , vol.6 , Issue.3 , pp. 221-251
    • Huang, M.1    Malhamé, R.P.2    Caines, P.E.3
  • 17
    • 80455173864 scopus 로고    scopus 로고
    • On a mean field game approach modeling congestion and aversion in pedestrian crowds
    • Lachapelle A., Wolfram M.-T. On a mean field game approach modeling congestion and aversion in pedestrian crowds. Transp. Res., Part B, Methodol. 2011, 45(10):1572-1589.
    • (2011) Transp. Res., Part B, Methodol. , vol.45 , Issue.10 , pp. 1572-1589
    • Lachapelle, A.1    Wolfram, M.-T.2
  • 18
    • 33750627999 scopus 로고    scopus 로고
    • Jeux à champ moyen. I. Le cas stationnaire
    • Lasry J.-M., Lions P.-L. Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 2006, 343(9):619-625.
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.9 , pp. 619-625
    • Lasry, J.-M.1    Lions, P.-L.2
  • 19
    • 33751077273 scopus 로고    scopus 로고
    • Jeux à champ moyen. II. Horizon fini et contrÔle optimal
    • Lasry J.-M., Lions P.-L. Jeux à champ moyen. II. Horizon fini et contrÔle optimal. C. R. Math. Acad. Sci. Paris 2006, 343(10):679-684.
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.10 , pp. 679-684
    • Lasry, J.-M.1    Lions, P.-L.2
  • 22
    • 51249172276 scopus 로고
    • Quelques remarques sur les problèmes elliptiques quasilinéaires du second ordre
    • Lions P.-L. Quelques remarques sur les problèmes elliptiques quasilinéaires du second ordre. J. Anal. Math. 1985, 45:234-254.
    • (1985) J. Anal. Math. , vol.45 , pp. 234-254
    • Lions, P.-L.1
  • 23
    • 0000973918 scopus 로고
    • On elliptic partial differential equations
    • Nirenberg L. On elliptic partial differential equations. Ann. Sc. Norm. Super. Pisa (3) 1959, 13:115-162.
    • (1959) Ann. Sc. Norm. Super. Pisa (3) , vol.13 , pp. 115-162
    • Nirenberg, L.1
  • 24
    • 84888865707 scopus 로고    scopus 로고
    • ε-Nash mean field game theory for nonlinear stochastic dynamical systems with major and minor agents
    • Nourian M., Caines P.E. ε-Nash mean field game theory for nonlinear stochastic dynamical systems with major and minor agents. SIAM J. Control Optim. 2013, 51(4):3302-3331.
    • (2013) SIAM J. Control Optim. , vol.51 , Issue.4 , pp. 3302-3331
    • Nourian, M.1    Caines, P.E.2
  • 25
    • 34047155861 scopus 로고
    • p estimates and regularity. I
    • p estimates and regularity. I. Am. J. Math. 1963, 85:1-13.
    • (1963) Am. J. Math. , vol.85 , pp. 1-13
    • Schechter, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.