A remark on minimal lagrangian diffeomorphisms and the Monge-Ampère equation

John Urbas

doi:10.1017/s0004972700039605

A remark on minimal lagrangian diffeomorphisms and the Monge-Ampère equation

John Urbas^*

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We construct a counterexample to a theorem of Jon Wolfson concerning the existence of globally smooth solutions of the second boundary value problem for Monge-Ampère equations in two dimensions, or equivalently, on the existence of minimal Lagrangian diffeomorphisms between simply connected domains in R². Copyright Clearance Centre, Inc.

Original language	English
Pages (from-to)	215-218
Number of pages	4
Journal	Bulletin of the Australian Mathematical Society
Volume	76
Issue number	2
DOIs	https://doi.org/10.1017/s0004972700039605
Publication status	Published - Oct 2007

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abstract = "We construct a counterexample to a theorem of Jon Wolfson concerning the existence of globally smooth solutions of the second boundary value problem for Monge-Amp{\`e}re equations in two dimensions, or equivalently, on the existence of minimal Lagrangian diffeomorphisms between simply connected domains in R2. Copyright Clearance Centre, Inc.",

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AB - We construct a counterexample to a theorem of Jon Wolfson concerning the existence of globally smooth solutions of the second boundary value problem for Monge-Ampère equations in two dimensions, or equivalently, on the existence of minimal Lagrangian diffeomorphisms between simply connected domains in R2. Copyright Clearance Centre, Inc.

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A remark on minimal lagrangian diffeomorphisms and the Monge-Ampère equation

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