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Volumn 10, Issue 3, 2017, Pages 411-439

On the weak theory for mean field games systems

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EID: 85028676686     PISSN: 19726724     EISSN: 21982759     Source Type: Journal    
DOI: 10.1007/s40574-016-0105-x     Document Type: Article
Times cited : (19)

References (37)
  • 1
    • 84858650669 scopus 로고    scopus 로고
    • Mean field games: Numerical methods for the planning problem
    • Achdou, Y., Camilli F., Capuzzo Dolcetta, I.: Mean field games: numerical methods for the planning problem. SIAM J. Control Opt. 50, 77-109 (2012)
    • (2012) SIAM J. Control Opt , vol.50 , pp. 77-109
    • Achdou, Y.1    Camilli, F.2    Capuzzo Dolcetta, I.3
  • 2
    • 77956048120 scopus 로고    scopus 로고
    • Mean field games: Numerical methods
    • 2679575 1217.91019
    • Achdou, Y., Capuzzo Dolcetta, I.: Mean field games: numerical methods. SIAM J. Numer. Anal. 48, 1136-1162 (2010)
    • (2010) SIAM J. Numer. Anal. , vol.48 , pp. 1136-1162
    • Achdou, Y.1    Capuzzo Dolcetta, I.2
  • 3
    • 84960841215 scopus 로고    scopus 로고
    • Convergence of a finite difference scheme to weak solutions of the system of partial differential equation arising in mean field games
    • 3452251 06540924
    • Achdou, Y., Porretta, A.: Convergence of a finite difference scheme to weak solutions of the system of partial differential equation arising in mean field games. SIAM J. Numer. Anal. 54, 161-186 (2016)
    • (2016) SIAM J. Numer. Anal. , vol.54 , pp. 161-186
    • Achdou, Y.1    Porretta, A.2
  • 5
    • 0000093666 scopus 로고
    • A version of the fundamental theorem for Young measures
    • Rascle, M., Serre, D., Slemrod, M. (eds.) Springer, Berlin
    • Ball, J.M.: A version of the fundamental theorem for Young measures. In: Rascle, M., Serre, D., Slemrod, M. (eds.) PDE's and continuum models of phase transitions, Lecture Notes in Physics, vol. 344, pp. 207-215. Springer, Berlin (1989)
    • (1989) PDE's and Continuum Models of Phase Transitions, Lecture Notes in Physics , vol.344 , pp. 207-215
    • Ball, J.M.1
  • 6
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • 1738163 0968.76069
    • Benamou, J.-D., Brennier, Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84, 375-393 (2000)
    • (2000) Numer. Math. , vol.84 , pp. 375-393
    • Benamou, J.-D.1    Brennier, Y.2
  • 9
    • 79551545976 scopus 로고    scopus 로고
    • Uniqueness for solutions of Fokker-Planck equations on infinite dimensional spaces
    • 2765423 1239.60051
    • Bogachev, V., Da Prato, G., Röckner, M.: Uniqueness for solutions of Fokker-Planck equations on infinite dimensional spaces. Comm. Partial Diff. Equ. 36, 925-939 (2011)
    • (2011) Comm. Partial Diff. Equ. , vol.36 , pp. 925-939
    • Bogachev, V.1    Da Prato, G.2    Röckner, M.3
  • 11
    • 84887524276 scopus 로고    scopus 로고
    • Long time average of first order mean field games and weak KAM theory
    • 3127145 1314.91043
    • Cardaliaguet, P.: Long time average of first order mean field games and weak KAM theory. Dyn. Games Appl. 3, 473-488 (2013)
    • (2013) Dyn. Games Appl. , vol.3 , pp. 473-488
    • Cardaliaguet, P.1
  • 14
    • 84942369075 scopus 로고    scopus 로고
    • Second order mean field games with degenerate diffusion and local coupling
    • 3399179 1344.49061
    • Cardaliaguet, P., Graber, P.J., Porretta, A., Tonon, D.: Second order mean field games with degenerate diffusion and local coupling. NoDEA 22, 1287-1317 (2015)
    • (2015) NoDEA , vol.22 , pp. 1287-1317
    • Cardaliaguet, P.1    Graber, P.J.2    Porretta, A.3    Tonon, D.4
  • 16
  • 17
    • 84978423911 scopus 로고    scopus 로고
    • Local regularity for mean-field games in the whole space
    • 3477897 1339.35326
    • Gomes, D., Pimentel, E.: Local regularity for mean-field games in the whole space. Minimax Theory Appl. 1, 65-82 (2016)
    • (2016) Minimax Theory Appl. , vol.1 , pp. 65-82
    • Gomes, D.1    Pimentel, E.2
  • 18
    • 84911982713 scopus 로고    scopus 로고
    • Time-dependent mean-field games in the subquadratic case
    • Gomes, D., Pimentel, E., Sànchez-Morgado, H.: Time-dependent mean-field games in the subquadratic case. Comm. Partial Differ. Equ. 40, 40-76 (2015)
    • (2015) Comm. Partial Differ. Equ , vol.40 , pp. 40-76
    • Gomes, D.1
  • 19
    • 84964380514 scopus 로고    scopus 로고
    • Time-dependent mean-field games in the superquadratic case
    • Gomes, D., Pimentel, E., Sànchez-Morgado, H.: Time-dependent mean-field games in the superquadratic case. ESAIM Control Optim. Calc. Var. 22, 562-580 (2016)
    • (2016) ESAIM Control Optim. Calc. Var , vol.22 , pp. 562-580
    • Gomes, D.1
  • 20
    • 84899464039 scopus 로고    scopus 로고
    • Mean field games models -a brief survey
    • 3195844 1314.91048
    • Gomes, D., Saùde, J.: Mean field games models -a brief survey. Dyn. Games Appl. 4, 110-154 (2014)
    • (2014) Dyn. Games Appl. , vol.4 , pp. 110-154
    • Gomes, D.1    Saùde, J.2
  • 21
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
    • 2346927 1136.91349
    • Huang, M., Caines, P.E., Malhamé, R.P.: Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Comm. Inf. Syst. 6, 221-251 (2006)
    • (2006) Comm. Inf. Syst. , vol.6 , pp. 221-251
    • Huang, M.1    Caines, P.E.2    Malhamé, R.P.3
  • 22
    • 51249191546 scopus 로고
    • Schrödinger operators with singular potentials
    • Proceedings of the International Symposium on Partial Differential Equations and the Geometry of Normed Linear Spaces (Jerusalem, 1972)
    • Kato T.: Schrödinger operators with singular potentials. Israel J. Math. 13(1972), 135-148 (1973). In: Proceedings of the International Symposium on Partial Differential Equations and the Geometry of Normed Linear Spaces (Jerusalem, 1972)
    • (1972) Israel J. Math , vol.13 , pp. 135-148
    • Kato, T.1
  • 25
    • 34047127341 scopus 로고    scopus 로고
    • Mean field games
    • 2295621 1156.91321
    • Lasry, J.-M., Lions, P.-L.: Mean field games. Jpn. J. Math. 2(1), 229-260 (2007)
    • (2007) Jpn. J. Math. , vol.2 , Issue.1 , pp. 229-260
    • Lasry, J.-M.1    Lions, P.-L.2
  • 27
    • 79960442068 scopus 로고    scopus 로고
    • Local estimates for parabolic equations with nonlinear gradient terms
    • Leonori, T., Petitta, F.: Local estimates for parabolic equations with nonlinear gradient terms, Calc. Var. P.D.E. 42, 153-187 (2011)
    • (2011) Calc. Var. P.D.E. , vol.42 , pp. 153-187
    • Leonori, T.1    Petitta, F.2
  • 28
    • 0003628399 scopus 로고    scopus 로고
    • Mathematical topics in fluid mechanics. Vol. 1. Incompressible models
    • Oxford Science Publications. The Clarendon Press, Oxford University Press, New York
    • Lions P.-L.: Mathematical topics in fluid mechanics. Vol. 1. Incompressible models. Oxford Lecture Series in Mathematics and its Applications, 3. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York (1996)
    • (1996) Oxford Lecture Series in Mathematics and Its Applications , vol.3
    • Lions, P.-L.1
  • 29
    • 84865537156 scopus 로고    scopus 로고
    • Accessed 13 Jan 2012
    • Lions, P.-L.: Cours au Collège de France. https://www.college-de-france.fr/site/pierre-louis-lions/-course.htm. Accessed 13 Jan 2012
    • Cours Au Collège de France
    • Lions, P.-L.1
  • 30
    • 0001730497 scopus 로고
    • Non-cooperative games
    • 43432 0045.08202
    • Nash, J.: Non-cooperative games. Ann. Math. 54, 286-295 (1951)
    • (1951) Ann. Math. , vol.54 , pp. 286-295
    • Nash, J.1
  • 31
    • 0033482299 scopus 로고    scopus 로고
    • Optimization, relaxation and Young measures
    • 1655480 0916.49011
    • Pedregal, P.: Optimization, relaxation and Young measures. Bull. Am. Math. Soc. 36, 27-58 (1999)
    • (1999) Bull. Am. Math. Soc. , vol.36 , pp. 27-58
    • Pedregal, P.1
  • 32
    • 0141496722 scopus 로고    scopus 로고
    • Existence results for nonlinear parabolic equations via strong convergence of truncations
    • Porretta, A.: Existence results for nonlinear parabolic equations via strong convergence of truncations. Ann. Mat. Pura Appl. 177(4), 143-172 (1999)
    • (1999) Ann. Mat. Pura Appl , vol.177 , Issue.4 , pp. 143-172
    • Porretta, A.1
  • 33
    • 84881613408 scopus 로고    scopus 로고
    • On the planning problem for a class of mean field games
    • Ser. I 351
    • Porretta, A.: On the planning problem for a class of mean field games. C. R. Acad. Sci. Paris, Ser. I 351, 457-462 (2013)
    • (2013) C. R. Acad. Sci. Paris , pp. 457-462
    • Porretta, A.1
  • 34
    • 84899459829 scopus 로고    scopus 로고
    • On the planning problem for the mean field games system
    • 3195848 1314.91021
    • Porretta, A.: On the planning problem for the mean field games system. Dyn. Games Appl. 4, 231-256 (2014)
    • (2014) Dyn. Games Appl. , vol.4 , pp. 231-256
    • Porretta, A.1
  • 35
    • 84925014244 scopus 로고    scopus 로고
    • Weak solutions to Fokker-Planck equations and mean field games
    • 3305653 1312.35168
    • Porretta, A.: Weak solutions to Fokker-Planck equations and mean field games. Arch. Rat. Mech. Anal. 216, 1-62 (2015)
    • (2015) Arch. Rat. Mech. Anal. , vol.216 , pp. 1-62
    • Porretta, A.1
  • 36
    • 84891285243 scopus 로고    scopus 로고
    • Long time versus steady state optimal control
    • 3124890 1287.49006
    • Porretta, A., Zuazua, E.: Long time versus steady state optimal control. Siam J. Control Optim. 51, 4242-4273 (2013)
    • (2013) Siam J. Control Optim. , vol.51 , pp. 4242-4273
    • Porretta, A.1    Zuazua, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.