WELL-POSEDNESS OF MEAN FIELD GAMES MASTER EQUATIONS INVOLVING NON-SEPARABLE LOCAL HAMILTONIANS

David M. Ambrose, Alpár R. Mészáros

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)2481-2523
Number of pages43
JournalTransactions of the American Mathematical Society
Volume376
Issue number4
DOIs
StatePublished - Jan 24 2023
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2023-04-05
Acknowledged KAUST grant number(s): ORA-2021-CRG10-4674.2
Acknowledgements: The authors wish to thank W. Gangbo his constant interest in this work and for his valuable feedback and comments that he gave at various stages during the preparation of the manuscript. This project was conceived at IPAM, UCLA and a part of it was done while both authors were members of the long program “High Dimensional Hamilton-Jacobi PDEs” in 2020. D.M.A. has been partially supported by the NSF grant DMS-1907684, A.R.M. has been partially supported by the Air Force grant FA9550-18-1-0502 and by the King Abdullah University of Science and Technology Research Funding (KRF) under Award No. ORA-2021-CRG10-4674.2.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • General Mathematics

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