What question did this study set out to answer?

The aim is to define weak solutions to the master equation of potential mean field games and prove their existence and uniqueness.

Weak Solutions to the Master Equation of Potential Mean Field Games

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This work proves existence and uniqueness of weak solutions in mean field games, implying broader applications in dynamic systems.

The aim is to define weak solutions to the master equation of potential mean field games and prove their existence and uniqueness.
Introduce weak solutions without monotonicity constraints
Adapt arguments for hyperbolic systems in an infinite-dimensional context
Assume periodic coefficients for easier analysis using Fourier coefficients
Rewrite master and Hamilton-Jacobi-Bellman equations as partial differential equations
Establish existence and uniqueness of displacement semi-concave functions solving the Hamilton-Jacobi-Bellman equation
Construct a probability measure leading to unique optimal trajectories for the mean field control problem
Show existence and uniqueness of possibly discontinuous weak solutions to the master equation

Cecchin et al. (2025) studied this question.

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