Existence for stationary mean-field games with congestion and quadratic Hamiltonians
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
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AbstractHere, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
CitationGomes DA, Mitake H (2015) Existence for stationary mean-field games with congestion and quadratic Hamiltonians. Nonlinear Differential Equations and Applications NoDEA. Available: http://dx.doi.org/10.1007/s00030-015-0349-7.
PublisherSpringer Science + Business Media