메뉴 건너뛰기




Volumn 33, Issue , 2019, Pages 221-246

Introduction to variational methods for viscous ergodic mean-field games with local coupling

Author keywords

Elliptic systems; Ergodic mean field games; Variational methods

Indexed keywords


EID: 85069795334     PISSN: 2281518X     EISSN: 22815198     Source Type: Book Series    
DOI: 10.1007/978-3-030-18921-1_5     Document Type: Chapter
Times cited : (17)

References (40)
  • 1
    • 0000049356 scopus 로고
    • p approach to the Dirichlet problem. I. Regularity theorems
    • p approach to the Dirichlet problem. I. Regularity theorems. Ann. Scuola Norm. Sup. Pisa (3) 13, 405–448 (1959)
    • (1959) Ann. Scuola Norm. Sup. Pisa , vol.13 , Issue.3 , pp. 405-448
    • Agmon, S.1
  • 2
    • 84887513526 scopus 로고    scopus 로고
    • The derivation of ergodic mean field game equations for several populations of players
    • M. Bardi, E. Feleqi, The derivation of ergodic mean field game equations for several populations of players. Dyn. Games Appl. 3(4), 523–536 (2013)
    • (2013) Dyn. Games Appl. , vol.3 , Issue.4 , pp. 523-536
    • Bardi, M.1    Feleqi, E.2
  • 4
    • 0035541168 scopus 로고    scopus 로고
    • Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations
    • G. Barles, P. E. Souganidis, Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations. SIAM J. Math. Anal. 32(6), 1311–1323 (2001)
    • (2001) SIAM J. Math. Anal. , vol.32 , Issue.6 , pp. 1311-1323
    • Barles, G.1    Souganidis, P.E.2
  • 5
    • 85030238377 scopus 로고    scopus 로고
    • Bellomo, Degond, Tadmor
    • Variational Mean Field Games, ed., Springer, Berlin
    • J.-D. Benamou, G. Carlier, F. Santambrogio, Variational Mean Field Games, ed. by Bellomo, Degond, Tadmor. Active Particles, vol. 1 (Springer, Berlin, 2017)
    • (2017) Active Particles , vol.1
    • Benamou, J.-D.1    Carlier, G.2    Santambrogio, F.3
  • 9
  • 13
    • 84992539178 scopus 로고    scopus 로고
    • First order mean field games with density constraints: Pressure equals price
    • P. Cardaliaguet, A.R. Mészáros, F. Santambrogio, First order mean field games with density constraints: pressure equals price. SIAM J. Control. Optim. 54(5), 2672–2709 (2016)
    • (2016) SIAM J. Control. Optim. , vol.54 , Issue.5 , pp. 2672-2709
    • Cardaliaguet, P.1    Mészáros, A.R.2    Santambrogio, F.3
  • 16
    • 85057980819 scopus 로고    scopus 로고
    • Concentration of ground states in stationary mean-field games systems
    • A. Cesaroni, M. Cirant, Concentration of ground states in stationary mean-field games systems. Anal. PDE 12(3), 737–787 (2019)
    • (2019) Anal. PDE , vol.12 , Issue.3 , pp. 737-787
    • Cesaroni, A.1    Cirant, M.2
  • 19
    • 84926524427 scopus 로고    scopus 로고
    • Multi-population mean field games systems with Neumann boundary conditions
    • M. Cirant, Multi-population mean field games systems with Neumann boundary conditions. J. Math. Pures Appl. (9) 103(5), 1294–1315 (2015)
    • (2015) J. Math. Pures Appl. (9) , vol.103 , Issue.5 , pp. 1294-1315
    • Cirant, M.1
  • 20
    • 84938751802 scopus 로고    scopus 로고
    • A generalization of the Hopf-Cole transformation for stationary mean field games systems
    • M. Cirant, A generalization of the Hopf-Cole transformation for stationary mean field games systems. C.R. Math. 353(9), 807–811 (2015)
    • (2015) C.R. Math. , vol.353 , Issue.9 , pp. 807-811
    • Cirant, M.1
  • 21
    • 84979000025 scopus 로고    scopus 로고
    • Stationary focusing mean-field games
    • M. Cirant, Stationary focusing mean-field games. Commun. Part. Diff. Eq. 41(8), 1324–1346 (2016)
    • (2016) Commun. Part. Diff. Eq. , vol.41 , Issue.8 , pp. 1324-1346
    • Cirant, M.1
  • 22
    • 85064014763 scopus 로고    scopus 로고
    • Time-dependent focusing mean-field games: The sub-critical case
    • M. Cirant, D. Tonon, Time-dependent focusing mean-field games: the sub-critical case. J. Dyn. Diff. Equat. 31(1), 49–79 (2019)
    • (2019) J. Dyn. Diff. Equat. , vol.31 , Issue.1 , pp. 49-79
    • Cirant, M.1    Tonon, D.2
  • 23
    • 85019614845 scopus 로고    scopus 로고
    • Bifurcation and segregation in quadratic two-populations mean field games systems
    • M. Cirant, G. Verzini, Bifurcation and segregation in quadratic two-populations mean field games systems. ESAIM Control Optim. Calc. Var. 23, 1145–1177 (2017)
    • (2017) ESAIM Control Optim. Calc. Var. , vol.23 , pp. 1145-1177
    • Cirant, M.1    Verzini, G.2
  • 25
    • 84887513526 scopus 로고    scopus 로고
    • The derivation of ergodic mean field game equations for several populations of players
    • E. Feleqi, The derivation of ergodic mean field game equations for several populations of players. Dyn. Games Appl. 3(4), 523–536 (2013)
    • (2013) Dyn. Games Appl. , vol.3 , Issue.4 , pp. 523-536
    • Feleqi, E.1
  • 26
    • 0003549965 scopus 로고    scopus 로고
    • Elliptic Partial Differential Equations of Second Order
    • Springer-Verlag, Berlin
    • D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Classics in Mathematics. (Springer-Verlag, Berlin, 2001)
    • (2001) Classics in Mathematics
    • Gilbarg, D.1    Trudinger, N.S.2
  • 27
    • 84899464039 scopus 로고    scopus 로고
    • Mean field games models–a brief survey
    • D.A. Gomes, J. Saude, Mean field games models–a brief survey. Dyn. Games Appl. 4(2), 110– 154 (2014)
    • (2014) Dyn. Games Appl. , vol.4 , Issue.2 , pp. 110-154
    • Gomes, D.A.1    Saude, J.2
  • 28
    • 84892860445 scopus 로고    scopus 로고
    • On the existence of classical solutions for stationary extended mean field games
    • D.A. Gomes, S. Patrizi, V. Voskanyan, On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal. 99, 49–79 (2014)
    • (2014) Nonlinear Anal , vol.99 , pp. 49-79
    • Gomes, D.A.1    Patrizi, S.2    Voskanyan, V.3
  • 29
    • 85045415487 scopus 로고    scopus 로고
    • One-dimensional stationary mean-field games with local coupling
    • D.A. Gomes, L. Nurbekyan, M. Prazeres, One-dimensional stationary mean-field games with local coupling. Dyn. Games Appl. 8(2), 315–351 (2018)
    • (2018) Dyn. Games Appl. , vol.8 , Issue.2 , pp. 315-351
    • Gomes, D.A.1    Nurbekyan, L.2    Prazeres, M.3
  • 31
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the nash certainty equivalence principle
    • M. Huang, R. Malhamé, P. Caines, Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the nash certainty equivalence principle. Commun. Inf. Syst. 6(3), 221–251 (2006)
    • (2006) Commun. Inf. Syst. , vol.6 , Issue.3 , pp. 221-251
    • Huang, M.1    Malhamé, R.2    Caines, P.3
  • 33
    • 0000104617 scopus 로고
    • Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints
    • J.-M. Lasry, P.-L. Lions, Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. Math. Ann. 283(4), 583–630 (1989)
    • (1989) Math. Ann. , vol.283 , Issue.4 , pp. 583-630
    • Lasry, J.-M.1    Lions, P.-L.2
  • 34
    • 33751077273 scopus 로고    scopus 로고
    • Jeux à champ moyen. II. Horizon fini et contrôle optimal
    • J.-M. Lasry, P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal. C. R. Math. Acad. Sci. Paris 343(10), 679–684 (2006)
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.10 , pp. 679-684
    • Lasry, J.-M.1    Lions, P.-L.2
  • 35
    • 33750627999 scopus 로고    scopus 로고
    • Jeux à champ moyen. I. Le cas stationnaire
    • J.-M. Lasry, P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343(9), 619–625 (2006)
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.9 , pp. 619-625
    • Lasry, J.-M.1    Lions, P.-L.2
  • 38
    • 84948110228 scopus 로고    scopus 로고
    • A variational approach to second order mean field games with density constraints: The stationary case
    • A.R. Mészáros, F.J. Silva, A variational approach to second order mean field games with density constraints: the stationary case. J. Math. Pures Appl. (9) 104(6), 1135–1159 (2015)
    • (2015) J. Math. Pures Appl. (9) , vol.104 , Issue.6 , pp. 1135-1159
    • Mészáros, A.R.1    Silva, F.J.2
  • 39
    • 85015147717 scopus 로고    scopus 로고
    • Regularity for second-order stationary mean-field games
    • E. Pimentel, V. Voskanyan, Regularity for second-order stationary mean-field games. Indiana Univ. Math. J. 66, 1–22 (2017)
    • (2017) Indiana Univ. Math. J. , vol.66 , pp. 1-22
    • Pimentel, E.1    Voskanyan, V.2
  • 40
    • 0000819314 scopus 로고
    • Integral functionals, normal integrands and measurable selections
    • R.T. Rockafellar, Integral functionals, normal integrands and measurable selections. Lect. Notes Math. 543, 157–207 (1976)
    • (1976) Lect. Notes Math. , vol.543 , pp. 157-207
    • Rockafellar, R.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.