Glaeser's type gradient estimates for non-negative solutions of fully nonlinear elliptic equations
Italo Capuzzo Dolcetta Antonio Vitolo
Discrete & Continuous Dynamical Systems - A 2010, 28(2): 539-557 doi: 10.3934/dcds.2010.28.539
In this paper we discuss some extensions to a fully nonlinear setting of results by Y.Y. Li and L. Nirenberg [25] about gradient estimates for non-negative solutions of linear elliptic equations. Our approach relies heavily on methods developed by L. Caffarelli in [3] and [4].
keywords: Maximum Principles Gradient estimates Elliptic equations Viscosity solutions.
Fabio Camilli Italo Capuzzo Dolcetta Maurizio Falcone
Networks & Heterogeneous Media 2012, 7(2): i-ii doi: 10.3934/nhm.2012.7.2i
The theory of Mean Field Games (MFG, in short) is a branch of the theory of Differential Games which aims at modeling and analyzing complex decision processes involving a large number of indistinguishable rational agents who have individually a very small influence on the overall system and are, on the other hand, influenced by the mass of the other agents. The name comes from particle physics where it is common to consider interactions among particles as an external mean field which influences the particles. In spite of the optimization made by rational agents, playing the role of particles in such models, appropriate mean field equations can be derived to replace the many particles interactions by a single problem with an appropriately chosen external mean field which takes into account the global behavior of the individuals.

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