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

David M. Ambrose; Alpár R. Mészáros

doi:10.1090/tran/8760

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

David M. Ambrose, Alpár R. Mészáros

Research output: Contribution to journal › Article › peer-review

5 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 language	English (US)
Pages (from-to)	2481-2523
Number of pages	43
Journal	Transactions of the American Mathematical Society
Volume	376
Issue number	4
DOIs	https://doi.org/10.1090/tran/8760
State	Published - Jan 24 2023
Externally published	Yes

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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10.1090/tran/8760

Cite this

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title = "WELL-POSEDNESS OF MEAN FIELD GAMES MASTER EQUATIONS INVOLVING NON-SEPARABLE LOCAL HAMILTONIANS",

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.",

author = "Ambrose, {David M.} and M{\'e}sz{\'a}ros, {Alp{\'a}r R.}",

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.",

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AU - Mészáros, Alpár R.

N1 - 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.

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N2 - 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.

AB - 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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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 4

ER -

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

Abstract

Bibliographical note

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