A Priori Bounds for Stationary Models

Diogo A. Gomes; Edgard A. Pimentel; Vardan Voskanyan

doi:10.1007/978-3-319-38934-9_7

A Priori Bounds for Stationary Models

Diogo A. Gomes^*, Edgard A. Pimentel, Vardan Voskanyan

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We draw upon our earlier results to study stationary MFGs. Here, we illustrate various techniques in three models. First, we use the Bernstein estimates given in Theorem 3.11, to obtain Sobolev estimates for the value function. Next, we consider a congestion problem and show, through a remarkable identity, that m > 0. Finally, we examine an MFG with a logarithmic nonlinearity. This model presents substantial challenges since the logarithm is not bounded from below. However, a clever integration by parts argument gives the necessary bounds for its study.

Original language	English (US)
Title of host publication	SpringerBriefs in Mathematics
Publisher	Springer Science and Business Media B.V.
Pages	97-103
Number of pages	7
DOIs	https://doi.org/10.1007/978-3-319-38934-9_7
State	Published - 2016

Publication series

Name	SpringerBriefs in Mathematics
ISSN (Print)	2191-8198
ISSN (Electronic)	2191-8201

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

Keywords

Bernstein Estimates
Logarithmic Nonlinearity
Present Substantial Challenges
Priori Bounds
Remarkable Identity

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-38934-9_7

Cite this

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title = "A Priori Bounds for Stationary Models",

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author = "Gomes, {Diogo A.} and Pimentel, {Edgard A.} and Vardan Voskanyan",

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TY - CHAP

T1 - A Priori Bounds for Stationary Models

AU - Gomes, Diogo A.

AU - Pimentel, Edgard A.

AU - Voskanyan, Vardan

PY - 2016

Y1 - 2016

N2 - We draw upon our earlier results to study stationary MFGs. Here, we illustrate various techniques in three models. First, we use the Bernstein estimates given in Theorem 3.11, to obtain Sobolev estimates for the value function. Next, we consider a congestion problem and show, through a remarkable identity, that m > 0. Finally, we examine an MFG with a logarithmic nonlinearity. This model presents substantial challenges since the logarithm is not bounded from below. However, a clever integration by parts argument gives the necessary bounds for its study.

AB - We draw upon our earlier results to study stationary MFGs. Here, we illustrate various techniques in three models. First, we use the Bernstein estimates given in Theorem 3.11, to obtain Sobolev estimates for the value function. Next, we consider a congestion problem and show, through a remarkable identity, that m > 0. Finally, we examine an MFG with a logarithmic nonlinearity. This model presents substantial challenges since the logarithm is not bounded from below. However, a clever integration by parts argument gives the necessary bounds for its study.

KW - Bernstein Estimates

KW - Logarithmic Nonlinearity

KW - Present Substantial Challenges

KW - Priori Bounds

KW - Remarkable Identity

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DO - 10.1007/978-3-319-38934-9_7

M3 - Chapter

AN - SCOPUS:85101073539

T3 - SpringerBriefs in Mathematics

SP - 97

EP - 103

BT - SpringerBriefs in Mathematics

PB - Springer Science and Business Media B.V.

ER -

A Priori Bounds for Stationary Models

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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