Mild and weak solutions of Mean Field Games problem for linear control systems

zbMath1454.35389arXiv1907.02654MaRDI QIDQ5131861

Cristian Mendico, Piermarco Cannarsa

Publication date: 9 November 2020

Full work available at URL: https://arxiv.org/abs/1907.02654

zbMATH Keywords

control systemsmean field gamesmean field games equilibriumsemiconcave estimates

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Set-valued and variational analysis (49J53) Applications of optimal control and differential games (49N90) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Mean field games (aspects of game theory) (91A16)

Related Items (10)

A Lagrangian Approach for Aggregative Mean Field Games of Controls with Mixed and Final Constraints ⋮ A variational approach to first order kinetic mean field games with local couplings ⋮ Nonsmooth mean field games with state constraints ⋮ Generic properties of first-order mean field games ⋮ A singular perturbation problem for mean field games of acceleration: application to mean field games of control ⋮ Convergence of some mean field games systems to aggregation and flocking models ⋮ Ergodic behavior of control and mean field games problems depending on acceleration ⋮ A Cucker--Smale Inspired Deterministic Mean Field Game with Velocity Interactions ⋮ Non coercive unbounded first order mean field games: the Heisenberg example ⋮ Control and optimal stopping mean field games: a linear programming approach

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