On a price formation free boundary model by Lasry and Lions

Luis A. Caffarelli; Peter A. Markowich; Jan-F. Pietschmann

doi:10.1016/j.crma.2011.05.011

On a price formation free boundary model by Lasry and Lions

Luis A. Caffarelli, Peter A. Markowich, Jan-F. Pietschmann

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

18 Scopus citations

Abstract

We discuss global existence and asymptotic behaviour of a price formation free boundary model introduced by Lasry and Lions in 2007. Our results are based on a construction which transforms the problem into the heat equation with specially prepared initial datum. The key point is that the free boundary present in the original problem becomes the zero level set of this solution. Using the properties of the heat operator we can show global existence, regularity and asymptotic results of the free boundary. 2011 Académie des sciences.

Original language	English (US)
Pages (from-to)	621-624
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	349
Issue number	11-12
DOIs	https://doi.org/10.1016/j.crma.2011.05.011
State	Published - Jun 2011
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: We acknowledge supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST), by the Leverhulme Trust via Kinetic and mean field partial differential models for socio-economic processes (PI Peter Markowich) and by the Royal Society through the Wolfson Research Merit Award of Peter Markowich. Luis Caffarelli acknowledges support from the Division of Mathematical Sciences of the NSF.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.crma.2011.05.011

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title = "On a price formation free boundary model by Lasry and Lions",

abstract = "We discuss global existence and asymptotic behaviour of a price formation free boundary model introduced by Lasry and Lions in 2007. Our results are based on a construction which transforms the problem into the heat equation with specially prepared initial datum. The key point is that the free boundary present in the original problem becomes the zero level set of this solution. Using the properties of the heat operator we can show global existence, regularity and asymptotic results of the free boundary. 2011 Acad{\'e}mie des sciences.",

author = "Caffarelli, {Luis A.} and Markowich, {Peter A.} and Jan-F. Pietschmann",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: We acknowledge supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST), by the Leverhulme Trust via Kinetic and mean field partial differential models for socio-economic processes (PI Peter Markowich) and by the Royal Society through the Wolfson Research Merit Award of Peter Markowich. Luis Caffarelli acknowledges support from the Division of Mathematical Sciences of the NSF. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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On a price formation free boundary model by Lasry and Lions

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