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Volumn 100, Issue 2, 2019, Pages 644-667

New estimates on the regularity of the pressure in density-constrained mean field games

Author keywords

35J50; 35Q91; 49K20 (primary)

Indexed keywords


EID: 85066889371     PISSN: 00246107     EISSN: 14697750     Source Type: Journal    
DOI: 10.1112/jlms.12245     Document Type: Article
Times cited : (6)

References (27)
  • 1
    • 38849176743 scopus 로고    scopus 로고
    • On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations
    • L. Ambrosio and A. Figalli, ‘On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations’, Calc. Var. Partial Differential Equations 31 (2008) 497–509.
    • (2008) Calc. Var. Partial Differential Equations , vol.31 , pp. 497-509
    • Ambrosio, L.1    Figalli, A.2
  • 2
    • 70349507985 scopus 로고    scopus 로고
    • Geodesics in the space of measure-preserving maps and plans
    • L. Ambrosio and A. Figalli, ‘Geodesics in the space of measure-preserving maps and plans’, Arch. Ration. Mech. Anal. 194 (2009) 421–462.
    • (2009) Arch. Ration. Mech. Anal. , vol.194 , pp. 421-462
    • Ambrosio, L.1    Figalli, A.2
  • 7
    • 0033483717 scopus 로고    scopus 로고
    • Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations
    • Y. Brenier, ‘Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations’, Comm. Pure Appl. Math. 52 (1999) 411–452.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 411-452
    • Brenier, Y.1
  • 8
    • 85068762191 scopus 로고    scopus 로고
    • available online at
    • P. Cardaliaguet, ‘Notes on mean field games’, 2013, available online at https://www.ceremade.dauphine.fr/~cardalia/MFG20130420.pdf
    • (2013) Notes on mean field games
    • Cardaliaguet, P.1
  • 9
    • 85028753869 scopus 로고    scopus 로고
    • Weak solutions for first order mean field games with local coupling
    • (eds, P. Bettiol, P. Cannarsa, G. Colombo, M. Motta, F. Rampazzo, Springer, Cham
    • P. Cardaliaguet, ‘Weak solutions for first order mean field games with local coupling’, Analysis and geometry in control theory and its applications (eds P. Bettiol, P. Cannarsa, G. Colombo, M. Motta and F. Rampazzo; Springer, Cham, 2015) 111–158.
    • (2015) Analysis and geometry in control theory and its applications , pp. 111-158
    • Cardaliaguet, P.1
  • 11
    • 84992539178 scopus 로고    scopus 로고
    • First order mean field games with density constraints: pressure equals price
    • P. Cardaliaguet, A. R. Mészáros and F. Santambrogio, ‘First order mean field games with density constraints: pressure equals price’, SIAM J. Control Optim. 54 (2016) 2672–2709.
    • (2016) SIAM J. Control Optim. , vol.54 , pp. 2672-2709
    • Cardaliaguet, P.1    Mészáros, A.R.2    Santambrogio, F.3
  • 13
    • 0003448545 scopus 로고    scopus 로고
    • 2nd edn, AMS Graduate Studies in Mathematics (, Birkhauser, Boston
    • L. C. Evans, Partial differential equations, 2nd edn, AMS Graduate Studies in Mathematics (Birkhauser, Boston, 2010).
    • (2010) Partial differential equations
    • Evans, L.C.1
  • 14
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
    • 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) 221–252.
    • (2006) Commun. Inf. Syst. , vol.6 , pp. 221-252
    • Huang, M.1    Malhamé, R.P.2    Caines, P.E.3
  • 15
    • 0032343437 scopus 로고    scopus 로고
    • The variational formulation of the Fokker-Planck equation
    • R. Jordan, D. Kinderlehrer and F. Otto, ‘The variational formulation of the Fokker-Planck equation’, SIAM J. Math. Anal. 29 (1998) 1–17.
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1-17
    • Jordan, R.1    Kinderlehrer, D.2    Otto, F.3
  • 16
    • 85032961223 scopus 로고    scopus 로고
    • Time-convexity of the entropy in the multiphasic formulation of the incompressible Euler equation
    • H. Lavenant, ‘Time-convexity of the entropy in the multiphasic formulation of the incompressible Euler equation’, Calc. Var. Partial Differential Equations 56 (2017) 170.
    • (2017) Calc. Var. Partial Differential Equations , vol.56 , pp. 170
    • Lavenant, H.1
  • 17
    • 33751077273 scopus 로고    scopus 로고
    • Jeux à champ moyen. II. Horizon fini et contrôle optimal
    • 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.
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , pp. 679-684
    • Lasry, J.-M.1    Lions, P.-L.2
  • 19
    • 85063290691 scopus 로고    scopus 로고
    • Optimal density evolution with congestion: L∞ bounds via flow interchange techniques and applications to variational Mean Field Games
    • H. Lavenant and F. Santambrogio, ‘Optimal density evolution with congestion: L∞ bounds via flow interchange techniques and applications to variational Mean Field Games’, Comm. Partial Differential Equations 43 (2018) 1761–1802.
    • (2018) Comm. Partial Differential Equations , vol.43 , pp. 1761-1802
    • Lavenant, H.1    Santambrogio, F.2
  • 21
    • 32544455667 scopus 로고    scopus 로고
    • The reconstruction problem for the Euler-Poisson system in cosmology
    • G. Loeper, 'The reconstruction problem for the Euler-Poisson system in cosmology', Arch. Ration. Mech. Anal. 179 (2006) 153–216.
    • (2006) Arch. Ration. Mech. Anal. , vol.179 , pp. 153-216
    • Loeper, G.1
  • 23
    • 84980088516 scopus 로고
    • A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations
    • J. Moser, ‘A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations’, Comm. Pure Appl. Math. 13 (1960) 457–468.
    • (1960) Comm. Pure Appl. Math. , vol.13 , pp. 457-468
    • Moser, J.1
  • 24
    • 84865563114 scopus 로고    scopus 로고
    • A modest proposal for MFG with density constraints
    • F. Santambrogio, 'A modest proposal for MFG with density constraints', Netw. Heterog. Media 7 (2012) 337–347.
    • (2012) Netw. Heterog. Media , vol.7 , pp. 337-347
    • Santambrogio, F.1
  • 27
    • 2442557820 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, RI
    • C. Villani, Topics in optimal transportation, vol. 58 (American Mathematical Society, Providence, RI, 2003).
    • (2003) Topics in optimal transportation , vol.58
    • Villani, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.