Regularity theory and weak solutions for mean-field game systems

Levon Nurbekyan
University of California, Los Angeles (UCLA)
Mathematics and Statistics

The weak solutions and related regularity theories for mean-field game systems (MFG) is a challenging subject. When the mean-field coupling is a nonlocal regularizing operator, the viscosity solutions theory for Hamilton-Jacobi-Bellman (HJB) equations extends naturally to the MFG setting, providing suitable weak solutions and regularity theories. On the other hand, when the mean-field coupling is a local operator, there are no general weak solutions and associated regularity theories. In this talk, I will try to review existing approaches and discuss the main challenges in generalizing these methods. Then I will talk about some ideas that may help to overcome these difficulties.

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