Mean field games with state constraints: from mild to pointwise solutions of the PDE system

DOI10.1007/s00526-021-01936-4zbMath1467.49023arXiv1812.11374OpenAlexW3161726592WikidataQ115386762 ScholiaQ115386762MaRDI QIDQ2029889

Rossana Capuani, Pierre Cardaliaguet, Piermarco Cannarsa

Publication date: 4 June 2021

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.11374

zbMATH Keywords

constraintsmean field gamesPDE system

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Applications of optimal control and differential games (49N90) Regularity of solutions in optimal control (49N60) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (15)

A Lagrangian Approach for Aggregative Mean Field Games of Controls with Mixed and Final Constraints ⋮ Random lifting of set-valued maps ⋮ Nonsmooth mean field games with state constraints ⋮ Multipopulation Minimal-Time Mean Field Games ⋮ Deterministic Mean Field Games with Control on the Acceleration and State Constraints ⋮ Random lift of set valued maps and applications to multiagent dynamics ⋮ Generic properties of first-order mean field games ⋮ Weak KAM approach to first-order mean field games with state constraints ⋮ On Mean Field Games models for exhaustible commodities trade ⋮ A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection ⋮ Mean field games and applications: numerical aspects ⋮ An introduction to mean field game theory ⋮ On the asymptotic nature of first order mean field games ⋮ Computational Methods for First-Order Nonlocal Mean Field Games with Applications ⋮ Mean field games under invariance conditions for the state space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Mean field games. I: The stationary case
• Mean field games. II: Finite horizon and optimal control
• Augmented Lagrangian methods for transport optimization, mean field games and degenerate elliptic equations
• Mean field games
• A semi-Lagrangian scheme for a modified version of the Hughes' model for Pedestrian flow
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• C\(^{1,1}\)-smoothness of constrained solutions in the calculus of variations with application to mean field games
• Flux-limited solutions and state constraints for quasi-convex Hamilton-Jacobi equations in multidimensional domains
• Existence and uniqueness for mean field games with state constraints
• Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
• First Order Mean Field Games with Density Constraints: Pressure Equals Price
• Partial differential equation models in macroeconomics
• Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks
• Superposition Principle for Differential Inclusions
• Regularity of the Eikonal Equation with Neumann Boundary Conditions in the Plane: Application to Fronts with Nonlocal Terms
• Weak Solutions for First Order Mean Field Games with Local Coupling
• Hamilton-Jacobi Equations with State Constraints
• Optimal Control with State-Space Constraint I
• Optimal Control with State-Space Constraint. II
• Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations
• A New Formulation of State Constraint Problems for First-Order PDEs
• Modeling Rationality to Control Self-Organization of Crowds: An Environmental Approach
• Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria

This page was built for publication: Mean field games with state constraints: from mild to pointwise solutions of the PDE system