Existence for stationary mean-field games with congestion and quadratic Hamiltonians

Diogo A. Gomes, Hiroyoshi Mitake

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

Here, 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
Original languageEnglish (US)
Pages (from-to)1897-1910
Number of pages14
JournalNonlinear Differential Equations and Applications NoDEA
Volume22
Issue number6
DOIs
StatePublished - Sep 3 2015

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