Published Paper

Inserted: 9 may 2021
Last Updated: 22 aug 2023

Journal: Trans. Amer. Math. Soc.
Year: 2023

Abstract:

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.

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