Finite difference methods for mean field games In Hamilton-Jacobi equations: approximations, numerical analysis and applications, Lecture Notes in Math, vol.2074, pp.1-47, 2013. ,
DOI : 10.1007/978-3-642-36433-4
URL : https://link.springer.com/content/pdf/bfm%3A978-3-642-36433-4%2F1.pdf
Hamilton???Jacobi equations constrained on networks, equations constrained on networks, pp.413-445, 2013. ,
DOI : 10.1007/BF01396221
URL : https://hal.archives-ouvertes.fr/hal-00656919
Mean Field Games: Numerical Methods, SIAM Journal on Numerical Analysis, vol.48, issue.3, pp.1136-1162, 2010. ,
DOI : 10.1137/090758477
URL : https://hal.archives-ouvertes.fr/hal-00392074
Hamilton???Jacobi equations for optimal control on junctions and networks, ESAIM: Control, Optimisation and Calculus of Variations, vol.21, issue.3, pp.876-899, 2015. ,
DOI : 10.1137/0324067
URL : https://hal.archives-ouvertes.fr/hal-00847210
Convergence of a Finite Difference Scheme to Weak Solutions of the System of Partial Differential Equations Arising in Mean Field Games, SIAM Journal on Numerical Analysis, vol.54, issue.1, pp.161-186, 2016. ,
DOI : 10.1137/15M1015455
Existence de solutions faibles pour des équations elliptiques quasi-linéaires à croissance quadratique In Nonlinear partial differential equations and their applications, Collège de France Seminar Res. Notes in Math, vol.84, pp.19-73, 1981. ,
Mixed and hybrid finite element methods, of Springer Series in Computational Mathematics, 1991. ,
DOI : 10.1007/978-1-4612-3172-1
Stationary Mean Field Games Systems Defined on Networks, SIAM Journal on Control and Optimization, vol.54, issue.2, pp.1085-1103, 2016. ,
DOI : 10.1137/15M1022082
URL : http://arxiv.org/pdf/1505.04953
The vanishing viscosity limit for Hamilton???Jacobi equations on networks, Journal of Differential Equations, vol.254, issue.10, pp.4122-4143, 2013. ,
DOI : 10.1016/j.jde.2013.02.013
URL : https://doi.org/10.1016/j.jde.2013.02.013
Notes on mean field games. preprint, 2011. ,
Probabilistic Theory of Mean Field Games with Applications I-II, 2017. ,
DOI : 10.1007/978-3-319-56436-4
Vertex control of flows in networks, Netw. Heterog. Media, vol.3, issue.4, pp.709-722, 2008. ,
Theory and practice of finite elements, Applied Mathematical Sciences, vol.159, 2004. ,
DOI : 10.1007/978-1-4757-4355-5
Homogenization of second order discrete model with local perturbation and application to traffic flow, Discrete Contin, Dyn. Syst, vol.37, issue.3, pp.1437-1487, 2017. ,
DOI : 10.3934/dcds.2017060
URL : https://doi.org/10.3934/dcds.2017060
Diffusion processes on graphs: stochastic differential equations, large deviation principle. Probab. Theory Related Fields, pp.181-220, 2000. ,
DOI : 10.1007/pl00008726
Diffusion Processes on Graphs and the Averaging Principle, The Annals of Probability, vol.21, issue.4, pp.2215-2245, 1993. ,
DOI : 10.1214/aop/1176989018
URL : http://doi.org/10.1214/aop/1176989018
Elliptic partial differential equations of second order, Classics in Mathematics, 2001. ,
DOI : 10.1007/978-3-642-96379-7
On the existence of classical solutions for stationary extended mean field games, Nonlinear Analysis: Theory, Methods & Applications, vol.99, pp.49-79, 2014. ,
DOI : 10.1016/j.na.2013.12.016
URL : http://arxiv.org/pdf/1305.2696
Local regularity for mean-field games in the whole space, Minimax Theory Appl, vol.1, issue.1, pp.65-82, 2016. ,
DOI : 10.1007/978-3-319-38934-9_11
Time-Dependent Mean-Field Games in the Subquadratic Case, Communications in Partial Differential Equations, vol.6, issue.68, pp.40-76, 2015. ,
DOI : 10.1007/s00526-010-0363-x
Mean Field Games and Applications, Paris- Princeton Lectures on Mathematical Finance 2010, pp.205-266, 2003. ,
DOI : 10.1007/978-3-642-14660-2_3
An Invariance Principle in Large Population Stochastic Dynamic Games, Journal of Systems Science and Complexity, vol.20, issue.1, pp.162-172, 2007. ,
DOI : 10.1080/17442508708833446
URL : http://people.math.carleton.ca/~mhuang/JSCC07.pdf
Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria, IEEE Transactions on Automatic Control, vol.52, issue.9, pp.1560-1571, 2007. ,
DOI : 10.1109/TAC.2007.904450
Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Commun. Inf. Syst, vol.6, issue.3, pp.221-251, 2006. ,
A Hamilton-Jacobi approach to junction problems and application to traffic flows, ESAIM: Control, Optimisation and Calculus of Variations, vol.19, issue.1, pp.129-166, 2013. ,
DOI : 10.1051/cocv/2012002
URL : https://hal.archives-ouvertes.fr/hal-00569010
Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks, Annales scientifiques de l'??cole normale sup??rieure, vol.50, issue.2, pp.357-448, 2017. ,
DOI : 10.24033/asens.2323
URL : https://hal.archives-ouvertes.fr/hal-00832545
Jeux ?? champ moyen. I ??? Le cas stationnaire, Comptes Rendus Mathematique, vol.343, issue.9, pp.619-625, 2006. ,
DOI : 10.1016/j.crma.2006.09.019
Jeux ?? champ moyen. II ??? Horizon fini et contr??le optimal, Comptes Rendus Mathematique, vol.343, issue.10, pp.343679-684, 2006. ,
DOI : 10.1016/j.crma.2006.09.018
Mean field games, Japanese Journal of Mathematics, vol.4, issue.1, pp.229-260, 2007. ,
DOI : 10.1016/j.crma.2006.09.018
URL : https://hal.archives-ouvertes.fr/hal-00667356
Viscosity solutions for junctions: well posedness and stability, Rendiconti Lincei - Matematica e Applicazioni, vol.27, issue.4, pp.535-545, 2016. ,
DOI : 10.4171/RLM/747
URL : http://arxiv.org/pdf/1608.03682
Well-posedness for multi-dimensional junction problems with Kirchoff-type conditions, Rendiconti Lincei - Matematica e Applicazioni, vol.28, issue.4, pp.807-816, 2017. ,
DOI : 10.4171/RLM/786
URL : http://arxiv.org/pdf/1704.04001
Weak Solutions to Fokker???Planck Equations and Mean Field Games, Archive for Rational Mechanics and Analysis, vol.146, issue.4, pp.1-62, 2015. ,
DOI : 10.1007/s13235-013-0080-0
On the weak theory for mean field games systems, Bollettino dell'Unione Matematica Italiana, vol.51, issue.1, pp.411-439, 2017. ,
DOI : 10.1137/130907239
Classical solvability of linear parabolic equations on networks, Journal of Differential Equations, vol.72, issue.2, pp.316-337, 1988. ,
DOI : 10.1016/0022-0396(88)90158-1