2013/05/13 by Diogo A. Gomes, Gomes, Diogo A., Stefania Patrizi +3 · 4 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Historical Economic and Social Studies #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1305.2696
openalex publication_date 2013/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider extended stationary mean field games, that is\nmean-field games which depend on the velocity field of the players. We prove\nvarious a-priori estimates which generalize the results for quasi-variational\nmean field games in [GPSM12]. In addition we use adjoint method techniques to\nobtain higher regularity bounds. Then we establish existence of smooth\nsolutions under fairly general conditions by applying the continuity method.\nWhen applied to standard stationary mean-field games as in [LL06a], [GSM11] or\n[GPSM12] this paper yields various new estimates and regularity properties not\navailable previously. We discuss additionally several examples where existence\nof classical solutions can be proved.\n