{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:45:11Z","timestamp":1772297111336,"version":"3.50.1"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319161174","type":"print"},{"value":"9783319161181","type":"electronic"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-16118-1_15","type":"book-chapter","created":{"date-parts":[[2015,7,24]],"date-time":"2015-07-24T14:10:40Z","timestamp":1437747040000},"page":"291-304","source":"Crossref","is-referenced-by-count":6,"title":["Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case"],"prefix":"10.1007","author":[{"given":"Diogo A.","family":"Gomes","sequence":"first","affiliation":[]},{"given":"Edgard A.","family":"Pimentel","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"15_CR1","doi-asserted-by":"crossref","unstructured":"Achdou, Y.: Finite difference methods for mean field games. In: Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications, pp. 1\u201347. Springer, Heidelberg (2013)","DOI":"10.1007\/978-3-642-36433-4_1"},{"issue":"3","key":"15_CR2","doi-asserted-by":"publisher","first-page":"1136","DOI":"10.1137\/090758477","volume":"48","author":"Y. Achdou","year":"2010","unstructured":"Achdou, Y., Capuzzo-Dolcetta, I.: Mean field games: numerical methods. SIAM J. Numer. Anal. 48(3), 1136\u20131162 (2010)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"15_CR3","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1137\/100790069","volume":"50","author":"Y. Achdou","year":"2012","unstructured":"Achdou, Y., Camilli, F., Capuzzo-Dolcetta, I.: Mean field games: numerical methods for the planning problem. SIAM J. Control Optim. 50(1), 77\u2013109 (2012)","journal-title":"SIAM J. Control Optim."},{"key":"15_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-8508-7","volume-title":"Mean Field Games and Mean Field Type Control Theory","author":"A. Bensoussan","year":"2013","unstructured":"Bensoussan, A., Frehse, J., Yam, P.: Mean Field Games and Mean Field Type Control Theory. Springer Briefs in Mathematics. Springer, New York (2013)"},{"key":"15_CR5","unstructured":"Cardaliaguet, P.: Notes on mean-field games. Technical report. www.ceremade.dauphine.fr (2013)"},{"issue":"4","key":"15_CR6","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/s13235-013-0091-x","volume":"3","author":"P. Cardaliaguet","year":"2013","unstructured":"Cardaliaguet, P.: Long time average of first order mean field games and weak KAM theory. Dyn. Games Appl. 3(4): 473\u2013488 (2013)","journal-title":"Dyn. Games Appl."},{"key":"15_CR7","unstructured":"Cardaliaguet, P.: Weak solutions for first order mean-field games with local coupling (2013, preprint)"},{"issue":"2","key":"15_CR8","doi-asserted-by":"publisher","first-page":"279","DOI":"10.3934\/nhm.2012.7.279","volume":"7","author":"P. Cardaliaguet","year":"2012","unstructured":"Cardaliaguet, P., Lasry, J.-M., Lions, P.-L., Porretta, A.: Long time average of mean field games. Netw. Heterogen. Media 7(2), 279\u2013301 (2012)","journal-title":"Netw. Heterogen. Media"},{"issue":"5","key":"15_CR9","doi-asserted-by":"publisher","first-page":"3558","DOI":"10.1137\/120904184","volume":"51","author":"P. Cardaliaguet","year":"2013","unstructured":"Cardaliaguet, P., Lasry, J.-M., Lions, P.-L., Porretta, A.: Long time average of mean field games with a nonlocal coupling. SIAM J. Control Optim. 51(5), 3558\u20133591 (2013)","journal-title":"SIAM J. Control Optim."},{"issue":"68","key":"15_CR10","first-page":"15","volume":"18","author":"R. Carmona","year":"2013","unstructured":"Carmona, R., Delarue, F.: Mean field forward-backward stochastic differential equations. Electron. Commun. Probab. 18(68), 15 (2013)","journal-title":"Electron. Commun. Probab."},{"issue":"4","key":"15_CR11","doi-asserted-by":"publisher","first-page":"2705","DOI":"10.1137\/120883499","volume":"51","author":"R. Carmona","year":"2013","unstructured":"Carmona, R., Delarue, F.: Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51(4), 2705\u20132734 (2013)","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"15_CR12","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s00526-002-0164-y","volume":"17","author":"L.C. Evans","year":"2003","unstructured":"Evans, L.C.: Some new PDE methods for weak KAM theory. Calc. Var. Partial Differ. Equ. 17(2), 159\u2013177 (2003)","journal-title":"Calc. Var. Partial Differ. Equ."},{"issue":"3","key":"15_CR13","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1007\/s00205-010-0307-9","volume":"197","author":"L.C. Evans","year":"2010","unstructured":"Evans, L.C.: Adjoint and compensated compactness methods for Hamilton-Jacobi PDE. Arch. Ration. Mech. Anal. 197(3), 1053\u20131088 (2010)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"1","key":"15_CR14","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/j.jmaa.2014.02.044","volume":"418","author":"R. Ferreira","year":"2014","unstructured":"Ferreira, R., Gomes, D.A.: On the convergence of finite state mean-field games through \u0393-convergence. J. Math. Anal. Appl. 418(1), 211\u2013230 (2014)","journal-title":"J. Math. Anal. Appl."},{"key":"15_CR15","unstructured":"Gomes, D., Patrizi, S.: Obstacle and weakly coupled systems problem in mean field games. Interfaces and Free Boundaries (2013, to appear)"},{"issue":"2","key":"15_CR16","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1007\/s13235-013-0099-2","volume":"4","author":"D. Gomes","year":"2014","unstructured":"Gomes, D., Sa\u00fade, J.: Mean field games models\u2014a brief survey. Dyn. Games Appl. 4(2), 110\u2013154 (2014)","journal-title":"Dyn. Games Appl."},{"issue":"2","key":"15_CR17","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1090\/S0002-9947-2013-05936-3","volume":"366","author":"D. Gomes","year":"2014","unstructured":"Gomes, D., S\u00e1nchez Morgado, H.: A stochastic Evans-Aronsson problem. Trans. Am. Math. Soc. 366(2), 903\u2013929 (2014)","journal-title":"Trans. Am. Math. Soc."},{"key":"15_CR18","unstructured":"Gomes, D., Voskanyan, V.: Extended mean-field games - formulation, existence, uniqueness and examples (2013, preprint)"},{"issue":"10","key":"15_CR19","doi-asserted-by":"publisher","first-page":"3591","DOI":"10.1090\/S0002-9939-10-10361-X","volume":"138","author":"D. Gomes","year":"2010","unstructured":"Gomes, D., Iturriaga, R., S\u00e1nchez-Morgado, H., Yu, Y.: Mather measures selected by an approximation scheme. Proc. Am. Math. Soc. 138(10), 3591\u20133601 (2010)","journal-title":"Proc. Am. Math. Soc."},{"issue":"2","key":"15_CR20","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1016\/j.matpur.2009.10.010","volume":"93","author":"D. Gomes","year":"2010","unstructured":"Gomes, D., Mohr, J., Souza, R.R.: Discrete time, finite state space mean field games. J. Math. Pures Appl. 93(2), 308\u2013328 (2010)","journal-title":"J. Math. Pures Appl."},{"issue":"2","key":"15_CR21","doi-asserted-by":"publisher","first-page":"303","DOI":"10.3934\/nhm.2012.7.303","volume":"7","author":"D.A. Gomes","year":"2012","unstructured":"Gomes, D.A., Pires, G.E., S\u00e1nchez-Morgado, H.: A-priori estimates for stationary mean-field games. Netw. Heterogen. Media 7(2), 303\u2013314 (2012)","journal-title":"Netw. Heterogen. Media"},{"issue":"1","key":"15_CR22","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s00245-013-9202-8","volume":"68","author":"D. Gomes","year":"2013","unstructured":"Gomes, D., Mohr, J., Souza, R.R.: Continuous time finite state mean-field games. Appl. Math. Opt. 68(1), 99\u2013143 (2013)","journal-title":"Appl. Math. Opt."},{"key":"15_CR23","unstructured":"Gomes, D., Pimentel, E., S\u00e1nchez-Morgado, H.: Time dependent mean-field games in the superquadratic case. To appear in ESAIM: Control, Optimisation and Calculus of Variations (ESAIM:COVC) (2013, preprint)"},{"key":"15_CR24","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.na.2013.12.016","volume":"99","author":"D. Gomes","year":"2014","unstructured":"Gomes, D., Patrizi, S., Voskanyan, V.: On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal. 99, 49\u201379 (2014)","journal-title":"Nonlinear Anal."},{"issue":"1","key":"15_CR25","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1080\/03605302.2014.903574","volume":"40","author":"D.A. Gomes","year":"2015","unstructured":"Gomes, D.A., Pimentel, E.A., S\u00e1nchez-Morgado, H.: Time dependent mean-field games in the subquadratic case. Communications in Partial Differential Equations. 40(1), 40\u201376 (2015)","journal-title":"Communications in Partial Differential Equations."},{"key":"15_CR26","unstructured":"Gu\u00e9ant, O.: Mean field games and applications to economics. Ph.D. Thesis, Universit\u00e9 Paris Dauphine (2009)"},{"key":"15_CR27","doi-asserted-by":"crossref","unstructured":"Gu\u00e9ant, O., Lasry, J. M., Lions, P. L.: Mean field games and applications. In: Paris-Princeton Lectures on Mathematical Finance 2010, pp. 205\u2013266. Springer, Berlin Heidelberg (2011)","DOI":"10.1007\/978-3-642-14660-2_3"},{"issue":"3","key":"15_CR28","doi-asserted-by":"crossref","first-page":"221","DOI":"10.4310\/CIS.2006.v6.n3.a5","volume":"6","author":"M. Huang","year":"2006","unstructured":"Huang, M., Malham\u00e9, R.P., Caines, P.E.: Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6(3), 221\u2013251 (2006)","journal-title":"Commun. Inf. Syst."},{"issue":"9","key":"15_CR29","doi-asserted-by":"publisher","first-page":"1560","DOI":"10.1109\/TAC.2007.904450","volume":"52","author":"M. Huang","year":"2007","unstructured":"Huang, M., Caines, P.E., Malham\u00e9, R.P.: Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized \u03b5-Nash equilibria. IEEE Trans. Automat. Control 52(9), 1560\u20131571 (2007)","journal-title":"IEEE Trans. Automat. Control"},{"issue":"04","key":"15_CR30","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1142\/S0218202510004349","volume":"20","author":"A. Lachapelle","year":"2010","unstructured":"Lachapelle, A., Salomon, J., Turinici, G.: Computation of mean field equilibria in economics. Math. Models Methods Appl. Sci. 20(04), 567\u2013588 (2010)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"9","key":"15_CR31","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1016\/j.crma.2006.09.019","volume":"343","author":"J.-M. Lasry","year":"2006","unstructured":"Lasry, J.-M., Lions, P.-L.: Jeux \u00e0 champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343(9), 619\u2013625 (2006)","journal-title":"I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris"},{"issue":"10","key":"15_CR32","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1016\/j.crma.2006.09.018","volume":"343","author":"J.-M. Lasry","year":"2006","unstructured":"Lasry, J.-M., Lions, P.-L.: Jeux \u00e0 champ moyen. II. Horizon fini et contr\u00f4le optimal. C. R. Math. Acad. Sci. Paris 343(10), 679\u2013684 (2006)","journal-title":"II. Horizon fini et contr\u00f4le optimal. C. R. Math. Acad. Sci. Paris"},{"issue":"1","key":"15_CR33","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s11537-007-0657-8","volume":"2","author":"J.-M. Lasry","year":"2007","unstructured":"Lasry, J.-M., Lions, P.-L.: Mean field games. Jpn. J. Math. 2(1), 229\u2013260 (2007)","journal-title":"Jpn. J. Math."},{"key":"15_CR34","unstructured":"Lasry, J.-M., Lions, P.-L., Gu\u00e9ant, O.: Application of mean field games to growth theory (2010, preprint)"},{"key":"15_CR35","unstructured":"Lions, P.-L.: College de France course on mean-field games (2007\u20132011)"},{"key":"15_CR36","unstructured":"Lions, P.-L.: Course on mean-field games. IMA, University of Minnesota. Video. http:\/\/www.ima.umn.edu\/2012-2013\/sw11.12-13.12\/ (2012)"},{"key":"15_CR37","volume-title":"Time dependent mean-field games","author":"E.A. Pimentel","year":"2013","unstructured":"Pimentel, E.A.: Time dependent mean-field games. IST-UL. Doctoral thesis, Lisbon (2013)"},{"issue":"2","key":"15_CR38","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s13235-013-0080-0","volume":"4","author":"A. Porretta","year":"2014","unstructured":"Porretta, A.: On the planning problem for the mean-field games system. Dyn. Games Appl. 4(2), 231\u2013256 (2014)","journal-title":"Dyn. Games Appl."}],"container-title":["CIM Series in Mathematical Sciences","Dynamics, Games and Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-16118-1_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T13:51:22Z","timestamp":1676469082000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-16118-1_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319161174","9783319161181"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-16118-1_15","relation":{},"ISSN":["2364-950X","2364-9518"],"issn-type":[{"value":"2364-950X","type":"print"},{"value":"2364-9518","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}