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

Ambrose, David M.; Mészáros, Alpár R.

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.

Citation

Ambrose, D. M., & Mészáros, A. R. (2023). Well-posedness of mean field games master equations involving non-separable local Hamiltonians. Transactions of the American Mathematical Society, 376(4), 2481-2523. https://doi.org/10.1090/tran/8760

• Journal Article Type: Article
• Acceptance Date: Apr 28, 2022
• Online Publication Date: Jan 24, 2023
• Publication Date: 2023
• Deposit Date: Jun 23, 2022
• Journal: Transactions of the American Mathematical Society
• Print ISSN: 0002-9947
• Electronic ISSN: 1088-6850
• Publisher: American Mathematical Society
• Volume: 376
• Issue: 4
• Pages: 2481-2523
• DOI: https://doi.org/10.1090/tran/8760
• Public URL: https://durham-repository.worktribe.com/output/1200196