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Volumn 60, Issue 3, 2021, Pages

Mean field games with state constraints: from mild to pointwise solutions of the PDE system

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EID: 85105566267     PISSN: 09442669     EISSN: 14320835     Source Type: Journal    
DOI: 10.1007/s00526-021-01936-4     Document Type: Article
Times cited : (50)

References (30)
  • 1
    • 84907863441 scopus 로고    scopus 로고
    • Partial differential equation models in macroeconomics
    • Achdou, Y., Buera, F.J., Lasry, J.-M., Lions, P.-L., Moll, B.: Partial differential equation models in macroeconomics. Philos. Trans. R. Soc. A 372(2028), 20130397 (2014) DOI: 10.1098/rsta.2013.0397
    • (2014) Philos. Trans. R. Soc. A , vol.372 , Issue.2028 , pp. 20130397
    • Achdou, Y.1    Buera, F.J.2    Lasry, J.-M.3    Lions, P.-L.4    Moll, B.5
  • 4
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • Benamou, J.D., Brenier, Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84, 375–393 (2000) DOI: 10.1007/s002110050002
    • (2000) Numer. Math. , vol.84 , pp. 375-393
    • Benamou, J.D.1    Brenier, Y.2
  • 5
    • 84941420139 scopus 로고    scopus 로고
    • Augmented Lagrangian methods for trasport optimization, mean field games and degenerate elliptic equations
    • Benamou, J.D., Carlier, G.: Augmented Lagrangian methods for trasport optimization, mean field games and degenerate elliptic equations. J. Opt. Theor. Appl. 167(1), 1–26 (2015) DOI: 10.1007/s10957-015-0725-9
    • (2015) J. Opt. Theor. Appl. , vol.167 , Issue.1 , pp. 1-26
    • Benamou, J.D.1    Carlier, G.2
  • 6
    • 85030238377 scopus 로고    scopus 로고
    • Variational Mean Field Games. In
    • Bellomo, N., Degond, P., Tadmor, E. (eds.)
    • Benamou, J.D., Carlier, G., Santambrogio, F.: Variational Mean Field Games. In: Bellomo, N., Degond, P., Tadmor, E. (eds.) Active Particles, vol. 1, pp. 141–171. Birkhäuser, Modeling and Simulation in Science, Engineering and Technology (2017)
    • (2017) Engineering and Technology , vol.1 , pp. 141-171
    • Benamou, J.D.1    Carlier, G.2    Santambrogio, F.3
  • 7
    • 0033483717 scopus 로고    scopus 로고
    • Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations
    • Brenier, Y.: Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Commun. Pure Appl. Math. 52(4), 411–452 (1999) DOI: 10.1002/(SICI)1097-0312(199904)52:4<411::AID-CPA1>3.0.CO;2-3
    • (1999) Commun. Pure Appl. Math. , vol.52 , Issue.4 , pp. 411-452
    • Brenier, Y.1
  • 8
    • 85059103630 scopus 로고    scopus 로고
    • Existence and uniqueness for Mean Field Games with state constraints
    • Cardaliaguet P, Porretta A, Salvarani F, (eds), Springer, Cham
    • Cannarsa, P., Capuani, R.: Existence and uniqueness for Mean Field Games with state constraints. In: Cardaliaguet, P., Porretta, A., Salvarani, F. (eds.) PDE Models for Multi-Agent Phenomena, vol. 28. Springer, Cham (2018) DOI: 10.1007/978-3-030-01947-1_3
    • (2018) PDE Models for Multi-Agent Phenomena , vol.28
    • Cannarsa, P.1    Capuani, R.2
  • 9
    • 85084822360 scopus 로고    scopus 로고
    • 1, 1 -smoothness of constrained solutions in the calculus of variations with application to mean field games
    • 1, 1 -smoothness of constrained solutions in the calculus of variations with application to mean field games. Math. Eng. 1(1), 174–203 (2018). 10.3934/Mine.2018.1.174 DOI: 10.3934/Mine.2018.1.174
    • (2018) Math. Eng. , vol.1 , Issue.1 , pp. 174-203
    • Cannarsa, P.1    Capuani, R.2    Cardaliaguet, P.3
  • 11
    • 0001731298 scopus 로고
    • On the singularities of the viscosity solutions to Hamilton-Jacobi-Bellman equation
    • Cannarsa, P., Soner, H.M.: On the singularities of the viscosity solutions to Hamilton-Jacobi-Bellman equation. Indiana Univ. Math. JI 36, 501 (1987) DOI: 10.1512/iumj.1987.36.36028
    • (1987) Indiana Univ. Math. JI , vol.36 , pp. 501
    • Cannarsa, P.1    Soner, H.M.2
  • 12
    • 84966227140 scopus 로고
    • Hamilton-Jacobi equations with state constraints
    • Capuzzo-Dolcetta, I., Lions, P.L.: Hamilton-Jacobi equations with state constraints. Trans. Am. Math. Soc. 318(2), 643–683 (1990) DOI: 10.1090/S0002-9947-1990-0951880-0
    • (1990) Trans. Am. Math. Soc. , vol.318 , Issue.2 , pp. 643-683
    • Capuzzo-Dolcetta, I.1    Lions, P.L.2
  • 13
    • 34249023043 scopus 로고    scopus 로고
    • Regularity of the eikonal equation with Neumann boundary conditions in the plane: application to fronts with nonlocal terms
    • Cardaliaguet, P., Marchi, C.: Regularity of the eikonal equation with Neumann boundary conditions in the plane: application to fronts with nonlocal terms. SIAM J. Control Optim. 45(3), 1017–1038 (2006) DOI: 10.1137/050635894
    • (2006) SIAM J. Control Optim. , vol.45 , Issue.3 , pp. 1017-1038
    • Cardaliaguet, P.1    Marchi, C.2
  • 15
    • 84992539178 scopus 로고    scopus 로고
    • First order mean field games with density constraints: pressure equals price
    • Cardaliaguet, P., Mészáros, A.R., Santambrogio, F.: First order mean field games with density constraints: pressure equals price. SIAM J. Control Optim. 54(5), 2672–2709 (2016) DOI: 10.1137/15M1029849
    • (2016) SIAM J. Control Optim. , vol.54 , Issue.5 , pp. 2672-2709
    • Cardaliaguet, P.1    Mészáros, A.R.2    Santambrogio, F.3
  • 16
    • 85029489058 scopus 로고    scopus 로고
    • A semi-lagrangian scheme for a modified version of the Hughes’ model for pedestrian flow
    • Carlini, E., Festa, A., Silva, F.J., Wolfram, M.-T.: A semi-lagrangian scheme for a modified version of the Hughes’ model for pedestrian flow. Dyn. Games Appl. 7(4), 683–705 (2017) DOI: 10.1007/s13235-016-0202-6
    • (2017) Dyn. Games Appl. , vol.7 , Issue.4 , pp. 683-705
    • Carlini, E.1    Festa, A.2    Silva, F.J.3    Wolfram, M.-T.4
  • 17
    • 85039774320 scopus 로고    scopus 로고
    • Superposition Principle for Differential Inclusions
    • Lirkov I, Margenov S, (eds), Lecture Notes Computer Science, Springer, Cham
    • Cavagnari, G., Marigonda, A., Piccoli, B.: Superposition Principle for Differential Inclusions. In: Lirkov, I., Margenov, S. (eds.) Large-Scale Scientific Computing, LSSC 2017. Lecture Notes in Computer Science, vol. 10665, pp. 201–209. Springer, Cham (2018)
    • (2018) Large-Scale Scientific Computing, LSSC 2017 , vol.10665 , pp. 201-209
    • Cavagnari, G.1    Marigonda, A.2    Piccoli, B.3
  • 19
    • 84928985117 scopus 로고    scopus 로고
    • Modeling rationality to control self-organization of crowds: an environmental approach
    • Cristiani, E., Priuli, F.S., Tosin, A.: Modeling rationality to control self-organization of crowds: an environmental approach. SIAM J. Appl. Math. 75(2), 605–629 (2015) DOI: 10.1137/140962413
    • (2015) SIAM J. Appl. Math. , vol.75 , Issue.2 , pp. 605-629
    • Cristiani, E.1    Priuli, F.S.2    Tosin, A.3
  • 20
    • 0003391813 scopus 로고
    • Allyn and Bacon, Inc., Boston
    • Dugundji, J.: Topology. Allyn and Bacon, Inc., Boston (1966)
    • (1966) Topology
    • Dugundji, J.1
  • 21
    • 85026490144 scopus 로고    scopus 로고
    • Flux-limited solutions and state constraints for quasi-convex Hamilton Jacobi equations in multidimensional domains
    • Guerand, J.: Flux-limited solutions and state constraints for quasi-convex Hamilton Jacobi equations in multidimensional domains. Nonlinear Anal. 162, 162–177 (2017) DOI: 10.1016/j.na.2017.06.008
    • (2017) Nonlinear Anal. , vol.162 , pp. 162-177
    • Guerand, J.1
  • 22
    • 34648831837 scopus 로고    scopus 로고
    • Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ϵ -Nash equilibria
    • Huang, M., Caines, P.E., Malhamé, R.P.: Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ϵ -Nash equilibria. IEEE Trans. Autom. Control 52(9), 1560–1571 (2007) DOI: 10.1109/TAC.2007.904450
    • (2007) IEEE Trans. Autom. Control , vol.52 , Issue.9 , pp. 1560-1571
    • Huang, M.1    Caines, P.E.2    Malhamé, R.P.3
  • 23
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainly equivalence principle
    • Huang, M., Malhamé, R.P., Caines, P.E.: Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainly equivalence principle. Commun. Inf. Syst. 6(3), 221–252 (2006)
    • (2006) Commun. Inf. Syst. , vol.6 , Issue.3 , pp. 221-252
    • Huang, M.1    Malhamé, R.P.2    Caines, P.E.3
  • 24
    • 0030107199 scopus 로고    scopus 로고
    • A new formulation of state constraint problems for first-order PDEs
    • Ishii, H., Koike, S.: A new formulation of state constraint problems for first-order PDEs. SIAM J. Control Optim. 34(2), 554–571 (1996) DOI: 10.1137/S0363012993250268
    • (1996) SIAM J. Control Optim. , vol.34 , Issue.2 , pp. 554-571
    • Ishii, H.1    Koike, S.2
  • 25
    • 85105588775 scopus 로고    scopus 로고
    • Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks
    • to appear
    • Imbert, C., Monneau, R.: Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks, Annales scientifiques de l?ENS, to appear, (2016)
    • (2016) Annales Scientifiques De L?Ens
    • Imbert, C.1    Monneau, R.2
  • 26
    • 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 343(9), 619–625 (2006) DOI: 10.1016/j.crma.2006.09.019
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.9 , pp. 619-625
    • Lasry, J.-M.1    Lions, P.-L.2
  • 27
    • 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 343(9), 679–684 (2006) DOI: 10.1016/j.crma.2006.09.018
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.9 , pp. 679-684
    • Lasry, J.-M.1    Lions, P.-L.2
  • 28
    • 34047127341 scopus 로고    scopus 로고
    • Mean field games
    • Lasry, J.-M., Lions, P.-L.: Mean field games. Jpn. J. Math. 2(1), 229–260 (2007) DOI: 10.1007/s11537-007-0657-8
    • (2007) Jpn. J. Math. , vol.2 , Issue.1 , pp. 229-260
    • Lasry, J.-M.1    Lions, P.-L.2
  • 29
    • 0022715502 scopus 로고
    • Optimal control with state-space constraint I
    • Soner, H.M.: Optimal control with state-space constraint I. SIAM J. Control Optim. 24(3), 552–561 (1986) DOI: 10.1137/0324032
    • (1986) SIAM J. Control Optim. , vol.24 , Issue.3 , pp. 552-561
    • Soner, H.M.1
  • 30
    • 0022806544 scopus 로고
    • Optimal control with state-space constraint. II
    • Soner, H.M.: Optimal control with state-space constraint. II. SIAM J. Control Optim. 24(6), 1110–1122 (1986) DOI: 10.1137/0324067
    • (1986) SIAM J. Control Optim. , vol.24 , Issue.6 , pp. 1110-1122
    • Soner, H.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.