In mean-field game theory, Nash equilibria are described through solutions of PDE systems coupling Hamilton-Jacobi and Fokker-Planck equations. When the models involve local functions of the density in the cost functionals, this leads to study PDEs in non-regular setting. In this context a good notion of weak solutions to MFG systems is crucial to characterize singular limits, asymptotic regimes etc. A typical example occurs for vanishing viscosity limits as well as for optimal transport problems with congestion effects.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
