Non coercive unbounded first order mean field games: the Heisenberg example

DOI10.1016/j.jde.2021.11.029zbMath1489.35284arXiv2112.15332OpenAlexW4200351256MaRDI QIDQ2062054

Claudio Marchi, Paola Mannucci, Nicoletta Tchou

Publication date: 22 December 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.15332

zbMATH Keywords

Fokker-Planck equationHeisenberg groupcontinuity equationfirst-order Hamilton-Jacobi equationsmean field gamesdegenerate optimal control problemHeisenberg-type groupsnoncoercive Hamiltonian

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Hamilton-Jacobi equations (35F21) Fokker-Planck equations (35Q84) Systems of nonlinear first-order PDEs (35F50) Mean field games (aspects of game theory) (91A16) PDEs in connection with mean field game theory (35Q89)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A subelliptic analogue of Aronson-Serrin's Harnack inequality
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Second order mean field games with degenerate diffusion and local coupling
• Mean field games. I: The stationary case
• Mean field games. II: Finite horizon and optimal control
• Mean field games
• Ergodic mean field games with Hörmander diffusions
• Optimal paths for a car that goes both forwards and backwards
• Non-coercive first order mean field games
• Deterministic mean field games with control on the acceleration
• Existence and uniqueness for mean field games with state constraints
• The Hopf-Lax formula in Carnot groups: a control theoretic approach
• Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
• Long time average of first order mean field games and weak KAM theory
• Regularity Theory for Mean-Field Game Systems
• Nonholonomic motion planning: steering using sinusoids
• Functional Analysis, Calculus of Variations and Optimal Control
• Uniqueness Results for Second-Order Bellman--Isaacs Equations under Quadratic Growth Assumptions and Applications
• Fokker–Planck–Kolmogorov Equations
• Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Mild and weak solutions of Mean Field Games problem for linear control systems
• Mean Field Games and Mean Field Type Control Theory
• Some uniqueness theorems for solutions of parabolic and elliptic partial differential equations in unbounded regions
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

This page was built for publication: Non coercive unbounded first order mean field games: the Heisenberg example