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

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David M. Ambrose and Alpár R. Mészáros
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## 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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## Additional Information

**David M. Ambrose**- Affiliation: Department of Mathematics, Drexel University, Philadelphia, Pennsylvania
- MR Author ID: 720777
- ORCID: 0000-0003-4753-0319
- Email: dma68@drexel.edu
**Alpár R. Mészáros**- Affiliation: Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, England
- Email: alpar.r.meszaros@durham.ac.uk
- Received by editor(s): May 18, 2021
- Received by editor(s) in revised form: April 28, 2022
- Published electronically: January 24, 2023
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**376**(2023), 2481-2523 - MSC (2020): Primary 49N80; Secondary 91A16, 35K40
- DOI: https://doi.org/10.1090/tran/8760
- MathSciNet review: 4557872