Calculus of Variations and Geometric Measure Theory
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D. M. Ambrose - A. R. Mészáros

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

created by mészáros on 09 May 2021
modified on 15 Jun 2022


Accepted Paper

Inserted: 9 may 2021
Last Updated: 15 jun 2022

Journal: Trans. Amer. Math. Soc.
Year: 2022


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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