Weak Solutions to Fokker–Planck Equations and Mean Field Games

By Alessio Porretta. 2015

167 citations recorded by the source corpus.

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Citations in the corpus

Regularity for second order stationary mean-field games (2015, background): “Well-posedness in the class of weak solutions have been recently investigated in [24] and [4].”
Second order mean field games with degenerate diffusion and local coupling (2014, background): “, [8, 17, 18, 19, 21, 12, 13, 22]) or by stochastic techniques (see, e.”
Wellposedness of Second Order Master Equations for Mean Field Games with Nonsmooth Data (2019, unknown): “3) in Porretta [61] and Cardaliaguet-Graber-Porretta-Tonon [17].”
Mean Field Games Models—A Brief Survey (2013, background): “In the case g ≥ 0, one can obtain the additional estimate By combining the estimates (17) and (18), Lions and Lasry in [70, 71] obtained existence of weak solutions for various mean-ﬁeld games; see also the forthcoming paper [83] and [22].”
Stationary focusing mean-field games (2016, methodology): “We stress that in our case the lack of increasing monotonicity of −f cuts off from a large class of general approaches that have been developed in the MFG literature, for example in [7, 36, 15].”
Time dependent mean-field games in the superquadratic case (2013, methodology): “These include numerical methods [2, 3, 36], applications in economics [32, 41] and environmental policy [36], finite state problems [17, 27, 28], explicit models [33, 45], obstacle-type problems [19], congestion [18, 25], extended mean-field games [24, 29], probabilistic methods [13, 14], long-time ”
Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games (2015, background): “There have been a number of existence and uniqueness theorems proved when V [m] depends on m both locally [23, 5, 4, 8, 7, 14, 15] and non-locally [6].”
Mean field games with congestion (2017, methodology): “We now collect some compactness properties for the family (uǫ,mǫ), which are mostly borrowed from [30].”