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

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

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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. © 2011 Académie des sciences.
Original languageEnglish (US)
Pages (from-to)841-844
Number of pages4
JournalComptes Rendus Mathematique
Issue number15-16
StatePublished - Jul 27 2011
Externally publishedYes

Bibliographical 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.

ASJC Scopus subject areas

  • Mathematics(all)


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