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Journal of Differential Equations, ISSN 0022-0396, 06/2019, Volume 266, Issue 12, pp. 8067 - 8093
For non-monotone single and two-populations time-dependent Mean-Field Game systems we obtain the existence of an infinite number of branches of non-trivial... 
Bifurcation | Instability | Multi-population Mean-Field Games | MATHEMATICS | SEGREGATION | MODELS
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 08/2016, Volume 41, Issue 8, pp. 1324 - 1346
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 05/2015, Volume 103, Issue 5, pp. 1294 - 1315
In this paper we discuss some existence and uniqueness results for multi-population stationary Mean Field Games systems with Neumann conditions at the... 
Multi-population models | Mean Field Games | Ergodic stochastic control | Mean field games | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED | Computer entertainment systems
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2014, Volume 52, Issue 6, pp. 4001 - 4026
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 01/2014, Volume 52, Issue 6, pp. 4001 - 4026
This paper is concerned with stochastic ergodic control problems where both the state and the control space are $\mathbb{R} delta $. We are interested in... 
Lyapunov functions | Approximation | Mathematical analysis | Control systems | Reflection | Boundaries | Optimization | Ergodic processes
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 01/2017, Volume 27, Issue 1, pp. 75 - 113
This paper introduces and analyzes some models in the framework of mean field games (MFGs) describing interactions between two populations motivated by the... 
finite difference methods | systems of parabolic equations | multi-populations models | Mean field games | segregation | large populations limit | NUMERICAL-METHODS | MATHEMATICS, APPLIED | RESIDENTIAL SEGREGATION | EQUATIONS | DYNAMICAL-SYSTEMS | CONVERGENCE | BOUNDARY | AGENTS | SEMI-LAGRANGIAN SCHEME
Journal Article
Comptes rendus - Mathématique, ISSN 1631-073X, 09/2015, Volume 353, Issue 9, pp. 807 - 811
In this note we propose a transformation that decouples stationary Mean-Field Games systems with superlinear Hamiltonians of the form |p|r′, r′>1, and turns... 
MATHEMATICS | REGULARITY | DEGENERATE ELLIPTIC-EQUATIONS | Computer entertainment systems
Journal Article
ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 07/2017, Volume 23, Issue 3, pp. 1145 - 1177
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 3/2019, Volume 31, Issue 1, pp. 49 - 79
We consider time-dependent viscous mean-field games systems in the case of local, decreasing and unbounded couplings. These systems arise in mean-field game... 
Non-uniqueness | Ordinary Differential Equations | 49N70 | Mathematics | Applications of Mathematics | Local decreasing coupling | Partial Differential Equations | 35K55 | Variational formulation of mean field games | MATHEMATICS | MATHEMATICS, APPLIED | Game theory | Analysis of PDEs
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 6/2015, Volume 22, Issue 3, pp. 427 - 447
In this paper the Dirichlet problem for the equation which prescribes the ith principal curvature of the graph of a function u is considered. A Comparison... 
53C42 | Principal curvature | Degenerate elliptic | Dirichlet Problem | 35J60 | Prescribed curvature equations | Analysis | 35J70 | Mathematics | 35J25 | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | NONLINEAR ELLIPTIC-EQUATIONS
Journal Article
Minimax Theory and its Applications, ISSN 2199-1413, 2018, Volume 3, Issue 2, pp. 227 - 260
Journal Article
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, ISSN 0036-1410, 2019, Volume 51, Issue 2, pp. 913 - 954
We establish existence and uniqueness of solutions to evolutive fractional mean field game systems with regularizing coupling for any order of the fractional... 
Bessel potential spaces on the torus | MATHEMATICS, APPLIED | mean field games | EQUATIONS | fractional Hamilton-Jacobi equation | SYSTEMS | MEAN-FIELD GAMES | fractional Fokker-Planck equation
Journal Article
Analysis and PDE, ISSN 2157-5045, 2018, Volume 12, Issue 3, pp. 737 - 787
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 02/2019, Volume 122, pp. 1 - 22
We provide an existence result for stationary fractional mean field game systems, with fractional exponent greater than 1/2. In the case in which the coupling... 
Fractional Kolmogorov–Fokker–Planck equation | Ergodic mean-field games | Fractional viscous Hamilton–Jacobi equation | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | LIPSCHITZ REGULARITY | EQUATIONS | Fractional | Fractional viscous Hamilton-Jacobi equation | Kolmogorov-Fokker-Planck equation
Journal Article
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, ISSN 0294-1449, 02/2020
Journal Article
Publicacions Matematiques, ISSN 0214-1493, 2017, Volume 61, Issue 2, pp. 529 - 575
For scalar fully nonlinear partial differential equations F(x, D(2)u(x)) = 0 with x is an element of Omega subset of R-N, we present a general theory for... 
Comparison principles | Perron’s method | Admissible viscosity solutions | Elliptic branches | EXISTENCE | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | elliptic branches | DUALITY | PRINCIPLE | admissible viscosity solutions | Perron's method
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 01/2014, Volume 52, Issue 6, pp. 4001 - 4026
Journal Article
11/2017
For non-monotone single and two-populations time-dependent Mean-Field Game systems we obtain the existence of an infinite number of branches of non-trivial... 
Mathematics - Analysis of PDEs
Journal Article
03/2020
In this paper we consider an optimal control problem for a large population of interacting agents with deterministic dynamics, aggregating potential and... 
Mathematics - Analysis of PDEs
Journal Article
01/2020
For $q>2, \gamma > 1$, we prove that maximal regularity of $L^q$ type holds for periodic solutions to $-\Delta u + |Du|^\gamma = f$ in $\mathbb{R}^d$, under... 
Mathematics - Analysis of PDEs
Journal Article
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