A-priori estimates for stationary mean-field games

Diogo A. Gomes; Gabriel E. Pires; Héector Sánchez-Morgado

doi:10.3934/nhm.2012.7.303

A-priori estimates for stationary mean-field games

Diogo A. Gomes^*, Gabriel E. Pires, Héector Sánchez-Morgado

^*Corresponding author for this work

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

34 Scopus citations

Abstract

In this paper we establish a new class of a-priori estimates for stationary mean-field games which have a quasi-variational structure. In particular we prove W^1,2 estimates for the value function u and that the players distribution m satises √W^1,2We discuss further results for powerlike nonlinearities and prove higher regularity if the space dimension is 2. In particular we also obtain in this last case W^2,p estimates for u.

Original language	English (US)
Pages (from-to)	303-314
Number of pages	12
Journal	Networks and Heterogeneous Media
Volume	7
Issue number	2
DOIs	https://doi.org/10.3934/nhm.2012.7.303
State	Published - Jun 2012
Externally published	Yes

Keywords

A-priori estimates
Mean field games
Variational and quasi-variational methods

ASJC Scopus subject areas

Statistics and Probability
General Engineering
Computer Science Applications
Applied Mathematics

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10.3934/nhm.2012.7.303

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abstract = "In this paper we establish a new class of a-priori estimates for stationary mean-field games which have a quasi-variational structure. In particular we prove W1,2 estimates for the value function u and that the players distribution m satises √W1,2We discuss further results for powerlike nonlinearities and prove higher regularity if the space dimension is 2. In particular we also obtain in this last case W2,p estimates for u.",

keywords = "A-priori estimates, Mean field games, Variational and quasi-variational methods",

author = "Gomes, {Diogo A.} and Pires, {Gabriel E.} and H{\'e}ector S{\'a}nchez-Morgado",

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AU - Gomes, Diogo A.

AU - Pires, Gabriel E.

AU - Sánchez-Morgado, Héector

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AB - In this paper we establish a new class of a-priori estimates for stationary mean-field games which have a quasi-variational structure. In particular we prove W1,2 estimates for the value function u and that the players distribution m satises √W1,2We discuss further results for powerlike nonlinearities and prove higher regularity if the space dimension is 2. In particular we also obtain in this last case W2,p estimates for u.

KW - A-priori estimates

KW - Mean field games

KW - Variational and quasi-variational methods

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DO - 10.3934/nhm.2012.7.303

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EP - 314

JO - Networks and Heterogeneous Media

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IS - 2

ER -

A-priori estimates for stationary mean-field games

Abstract

Keywords

ASJC Scopus subject areas

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