Well-posedness of mean field games master equations involving non-separable local Hamiltonians

Understand

In this paper we construct short time classical solutions to a class of master equations in the presence of non-degenerate individual noise arising in the theory of mean field games.

• The considered Hamiltonians are non-separable and $local$ functions of the measure variable, therefore the equation is restricted to absolutely continuous measures whose densities lie in suitable Sobolev spaces.
• Our results hold for smooth enough Hamiltonians, without any additional structural conditions as convexity or monotonicity.