On a price formation free boundary model by Lasry and Lions: The Neumann problem

Luis A. Caffarelli; Peter A. Markowich; Marie Therese Wolfram

doi:10.1016/j.crma.2011.07.006

On a price formation free boundary model by Lasry and Lions: The Neumann problem

Luis A. Caffarelli^*, Peter A. Markowich, Marie Therese Wolfram

^*Corresponding author for this work

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

12 Scopus citations

Abstract

We discuss local and global existence and uniqueness for the price formation free boundary model with homogeneous Neumann boundary conditions introduced by Lasry and Lions in 2007. The results are based on a transformation of the problem to the heat equation with nonstandard boundary conditions. The free boundary becomes the zero level set of the solution of the heat equation. The transformation allows us to construct an explicit solution and discuss the behavior of the free boundary. Global existence can be verified under certain conditions on the free boundary and examples of non-existence are given.

Original language	English (US)
Pages (from-to)	841-844
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	349
Issue number	15-16
DOIs	https://doi.org/10.1016/j.crma.2011.07.006
State	Published - Aug 2011
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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@article{85b7cb6d43954185984ae2390ee2e9cd,

title = "On a price formation free boundary model by Lasry and Lions: The Neumann problem",

abstract = "We discuss local and global existence and uniqueness for the price formation free boundary model with homogeneous Neumann boundary conditions introduced by Lasry and Lions in 2007. The results are based on a transformation of the problem to the heat equation with nonstandard boundary conditions. The free boundary becomes the zero level set of the solution of the heat equation. The transformation allows us to construct an explicit solution and discuss the behavior of the free boundary. Global existence can be verified under certain conditions on the free boundary and examples of non-existence are given.",

author = "Caffarelli, {Luis A.} and Markowich, {Peter A.} and Wolfram, {Marie Therese}",

note = "KAUST Repository Item: Exported on 2021-07-01 Acknowledgements: P.M. acknowledges support by the King Abdullah University of Science and Technology, the Leverhulme Trust and the Royal Society. L.C. acknowledges support from the Division of Mathematical Sciences of the NSF, M.T.W. from the Austrian Science Foundation FWF. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2011",

month = aug,

doi = "10.1016/j.crma.2011.07.006",

language = "English (US)",

volume = "349",

pages = "841--844",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

publisher = "Academie des sciences",

number = "15-16",

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TY - JOUR

T1 - On a price formation free boundary model by Lasry and Lions

T2 - The Neumann problem

AU - Caffarelli, Luis A.

AU - Markowich, Peter A.

AU - Wolfram, Marie Therese

N1 - KAUST Repository Item: Exported on 2021-07-01 Acknowledgements: P.M. acknowledges support by the King Abdullah University of Science and Technology, the Leverhulme Trust and the Royal Society. L.C. acknowledges support from the Division of Mathematical Sciences of the NSF, M.T.W. from the Austrian Science Foundation FWF. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2011/8

Y1 - 2011/8

N2 - We discuss local and global existence and uniqueness for the price formation free boundary model with homogeneous Neumann boundary conditions introduced by Lasry and Lions in 2007. The results are based on a transformation of the problem to the heat equation with nonstandard boundary conditions. The free boundary becomes the zero level set of the solution of the heat equation. The transformation allows us to construct an explicit solution and discuss the behavior of the free boundary. Global existence can be verified under certain conditions on the free boundary and examples of non-existence are given.

AB - We discuss local and global existence and uniqueness for the price formation free boundary model with homogeneous Neumann boundary conditions introduced by Lasry and Lions in 2007. The results are based on a transformation of the problem to the heat equation with nonstandard boundary conditions. The free boundary becomes the zero level set of the solution of the heat equation. The transformation allows us to construct an explicit solution and discuss the behavior of the free boundary. Global existence can be verified under certain conditions on the free boundary and examples of non-existence are given.

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DO - 10.1016/j.crma.2011.07.006

M3 - Article

AN - SCOPUS:80052137565

SN - 1631-073X

VL - 349

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 15-16

ER -

On a price formation free boundary model by Lasry and Lions: The Neumann problem

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