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

created by mészáros on 09 May 2021

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Preprint

Inserted: 9 may 2021
Last Updated: 9 may 2021

Year: 2021

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.