메뉴 건너뛰기




Volumn 66, Issue 1, 2017, Pages 1-22

Regularity for second-order stationary mean-field games

Author keywords

A priori estimates; Existence of classical solutions; Integral bernstein method; Mean field games

Indexed keywords


EID: 85015147717     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2017.66.5944     Document Type: Article
Times cited : (35)

References (24)
  • 2
    • 84911092308 scopus 로고    scopus 로고
    • Linear-quadratic N-person and mean-field games with ergodic cost
    • MR3264562
    • M. BARDI and F. S. PRIULI, Linear-quadratic N-person and mean-field games with ergodic cost, SIAM J. Control Optim. 52(2014), no. 5, 3022-3052. http://dx.doi.org/10.1137/140951795. MR3264562
    • (2014) SIAM J. Control Optim. , vol.52 , Issue.5 , pp. 3022-3052
    • Bardi, M.1    Priuli, F.S.2
  • 4
    • 84942369075 scopus 로고    scopus 로고
    • Second order mean field games with degenerate diffusion and local coupling
    • MR3399179
    • P. CARDALIAGUET, P. J. GRABER, A. PORRETTA, and D. TONON, Second order mean field games with degenerate diffusion and local coupling, NoDEA Nonlinear Differential Equations Appl. 22(2015), no. 5, 1287-1317. http://dx.doi.org/10.1007/s00030-015-0323-4. MR3399179
    • (2015) NoDEA Nonlinear Differential Equations Appl. , vol.22 , Issue.5 , pp. 1287-1317
    • Cardaliaguet, P.1    Graber, P.J.2    Porretta, A.3    Tonon, D.4
  • 5
    • 84865574440 scopus 로고    scopus 로고
    • Long time average of mean field games
    • MR2928380
    • P. CARDALIAGUET, J. M. LASRY, P. L. LIONS, and A. PORRETTA, Long time average of mean field games, Netw. Heterog. Media 7(2012), no. 2, 279-301. http://dx.doi.org/10.3934/nhm.2012.7.279. MR2928380
    • (2012) Netw. Heterog. Media , vol.7 , Issue.2 , pp. 279-301
    • Cardaliaguet, P.1    Lasry, J.M.2    Lions, P.L.3    Porretta, A.4
  • 6
    • 84890470397 scopus 로고    scopus 로고
    • Long time average of mean field games with a nonlocal coupling
    • MR3103242
    • -, Long time average of mean field games with a nonlocal coupling, SIAM J. Control Optim. 51(2013), no. 5, 3558-3591. http://dx.doi.org/10.1137/120904184. MR3103242
    • (2013) SIAM J. Control Optim. , vol.51 , Issue.5 , pp. 3558-3591
    • Cardaliaguet, P.1    Lasry, J.M.2    Lions, P.L.3    Porretta, A.4
  • 7
    • 84926524427 scopus 로고    scopus 로고
    • Multi-population mean field games systems with Neumann boundary conditions
    • English, with English and French summaries, MR3333058
    • M. CIRANT, Multi-population mean field games systems with Neumann boundary conditions, J. Math. Pures Appl. (9) 103(2015), no. 5, 1294-1315 (English, with English and French summaries). http://dx.doi.org/10.1016/j.matpur.2014.10.013. MR3333058
    • (2015) J. Math. Pures Appl. (9) , vol.103 , Issue.5 , pp. 1294-1315
    • Cirant, M.1
  • 8
    • 0003979176 scopus 로고
    • Pure and Applied Mathematics, Academic Press, New York-London, Enlarged and corrected printing, MR0349288
    • J. DIEUDONNE, Foundations of Modern Analysis, Pure and Applied Mathematics, vol. 10-I, Academic Press, New York-London, 1969. Enlarged and corrected printing. MR0349288
    • (1969) Foundations of Modern Analysis , vol.10-11
    • Dieudonne, J.1
  • 9
    • 84887513526 scopus 로고    scopus 로고
    • The derivation of ergodic mean field game equations for several populations of players
    • MR3127148
    • E. FELEQI, The derivation of ergodic mean field game equations for several populations of players, Dyn. Games Appl. 3(2013), no. 4, 523-536. http://dx.doi.org/10.1007/s13235-013-0088-5. MR3127148
    • (2013) Dyn. Games Appl. , vol.3 , Issue.4 , pp. 523-536
    • Feleqi, E.1
  • 10
    • 84945453305 scopus 로고    scopus 로고
    • Existence for stationary mean-field games with congestion and quadratic Hamiltonians
    • MR3415027
    • D. A. GOMES and H. MITAKE, Existence for stationary mean-field games with congestion and quadratic Hamiltonians, NoDEA Nonlinear Differential Equations Appl. 22(2015), no. 6, 1897-1910. http://dx.doi.org/10.1007/s00030-015-0349-7. MR3415027
    • (2015) NoDEA Nonlinear Differential Equations Appl. , vol.22 , Issue.6 , pp. 1897-1910
    • Gomes, D.A.1    Mitake, H.2
  • 11
    • 84892860445 scopus 로고    scopus 로고
    • On the existence of classical solutions for stationary extended mean field games
    • MR3160525
    • D. A. GOMES, S. PATRIZI, and V. VOSKANYAN, On the existence of classical solutions for stationary extended mean field games, Nonlinear Anal. 99(2014), 49-79. http://dx.doi.org/10.1016/j.na.2013.12.016. MR3160525
    • (2014) Nonlinear Anal. , vol.99 , pp. 49-79
    • Gomes, D.A.1    Patrizi, S.2    Voskanyan, V.3
  • 12
    • 84947474862 scopus 로고    scopus 로고
    • Time-dependent mean-field games with logarithmic nonlinearities
    • MR3404683
    • D. A. GOMES and E. A. PIMENTEL, Time-dependent mean-field games with logarithmic nonlinearities, SIAM J. Math. Anal. 47(2015), no. 5, 3798-3812. http://dx.doi.org/10.1137/140984622. MR3404683
    • (2015) SIAM J. Math. Anal. , vol.47 , Issue.5 , pp. 3798-3812
    • Gomes, D.A.1    Pimentel, E.A.2
  • 13
    • 84964380514 scopus 로고    scopus 로고
    • Time-dependent mean-field games in the superquadratic case
    • MR3491784
    • D. A. GOMES, E. A. PIMENTEL, and H. SANCHEZ-MORGADO, Time-dependent mean-field games in the superquadratic case, ESAIM Control Optim. Calc. Var. 22(2016), no. 2, 562-580. http://dx.doi.org/10.1051/cocv/2015029. MR3491784
    • (2016) ESAIM Control Optim. Calc. Var. , vol.22 , Issue.2 , pp. 562-580
    • Gomes, D.A.1    Pimentel, E.A.2    Sanchez-Morgado, H.3
  • 15
    • 84865604666 scopus 로고    scopus 로고
    • A-priori estimates for stationary mean-field games
    • MR2928381
    • D. A. GOMES, G. E. PIRES, and H. SANCHEZ-MORGADO, A-priori estimates for stationary mean-field games, Netw. Heterog. Media 7(2012), no. 2, 303-314. http://dx.doi.org/10.3934/nhm.2012.7.303. MR2928381
    • (2012) Netw. Heterog. Media , vol.7 , Issue.2 , pp. 303-314
    • Gomes, D.A.1    Pires, G.E.2    Sanchez-Morgado, H.3
  • 16
    • 84888089068 scopus 로고    scopus 로고
    • A stochastic Evans-Aronsson problem
    • MR3130321
    • D. GOMES and H. SANCHEZ MORGADO, A stochastic Evans-Aronsson problem, Trans. Amer. Math. Soc. 366(2014), no. 2, 903-929. http://dx.doi.org/10.1090/S0002-9947-2013-05936-3. MR3130321
    • (2014) Trans. Amer. Math. Soc. , vol.366 , Issue.2 , pp. 903-929
    • Gomes, D.1    Sanchez Morgado, H.2
  • 17
    • 33750627999 scopus 로고    scopus 로고
    • Jeux a champ moyen. I: Le cas stationnaire
    • French, with English and French summaries, MR2269875
    • J. M. LASRY and P. L. LIONS, Jeux a champ moyen. I: Le cas stationnaire, C. R. Math. Acad. Sci. Paris 343(2006), no. 9, 619-625 (French, with English and French summaries). http://dx.doi.org/10.1016/j.crma.2006.09.019. MR2269875
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.9 , pp. 619-625
    • Lasry, J.M.1    Lions, P.L.2
  • 18
    • 33751077273 scopus 로고    scopus 로고
    • Jeux a champ moyen. II: Horizon fini et controle optimal
    • French, with English and French summaries, MR2271747
    • -, Jeux a champ moyen. II: Horizon fini et controle optimal, C. R. Math. Acad. Sci. Paris 343(2006), no. 10, 679-684 (French, with English and French summaries). http://dx.doi.org/10.1016/j.crma.2006.09.018. MR2271747
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.10 , pp. 679-684
    • Lasry, J.M.1    Lions, P.L.2
  • 19
    • 34047127341 scopus 로고    scopus 로고
    • Mean fieldgames
    • MR2295621
    • -, Mean fieldgames, Jpn. J. Math. 2(2007), no. 1, 229-260. http://dx.doi.org/10.1007/s11537-007-0657-8. MR2295621
    • (2007) Jpn. J. Math. , vol.2 , Issue.1 , pp. 229-260
    • Lasry, J.M.1    Lions, P.L.2
  • 20
    • 0003444739 scopus 로고
    • Die Grundlehren der mathematischen Wissenschaften Fundamental Principles of Mathematical Sciences, Springer-Verlag, New York-Berlin, Translated from the French by S. K. Mitter, MR0271512
    • J. L. LIONS, Optimal Control of Systems Governed by Partial Differential Equations, Die Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 170, Springer-Verlag, New York-Berlin, 1971. Translated from the French by S. K. Mitter. MR0271512
    • (1971) Optimal Control of Systems Governed by Partial Differential Equations , vol.170
    • Lions, J.L.1
  • 21
    • 51249172276 scopus 로고
    • Quelques remarquessur lesproblèmes elliptiques quasilinéaires du secondordre
    • French, MR833413
    • P. L. LIONS, Quelques remarquessur lesproblèmes elliptiques quasilinéaires du secondordre, J. Analyse Math. 45(1985), 234-254 (French). http://dx.doi.org/10.1007/BF02792551. MR833413
    • (1985) J. Analyse Math. , vol.45 , pp. 234-254
    • Lions, P.L.1
  • 23
    • 84899459829 scopus 로고    scopus 로고
    • On the planning problem for the mean field games system
    • MR3195848
    • A. PORRETTA, On the planning problem for the mean field games system, Dyn. Games Appl. 4(2014), no. 2, 231-256. http://dx.doi.org/10.1007/s13235-013-0080-0. MR3195848
    • (2014) Dyn. Games Appl. , vol.4 , Issue.2 , pp. 231-256
    • Porretta, A.1
  • 24
    • 84925014244 scopus 로고    scopus 로고
    • Weak solutions to Fokker-Planck equations and mean field games
    • MR3305653
    • -, Weak solutions to Fokker-Planck equations and mean field games, Arch. Ration. Mech. Anal. 216(2015), no. 1, 1-62. http://dx.doi.org/10.1007/s00205-014-0799-9. MR3305653
    • (2015) Arch. Ration. Mech. Anal. , vol.216 , Issue.1 , pp. 1-62
    • Porretta, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.