descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 2000 English Publisher:Springer Science and Business Media LLCJournal:Journal d'Analyse Mathématique, volume 80, pages 37-86 (issn: 0021-7670, eissn: 1565-8538,

Authors: Bourgain, Jean; Brezis, Haïm; Mironescu, Petru;

doi: 10.1007/bf02791533

Lifting in Sobolev spaces

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Abstract

We characterize the couples $(s,p)$ with the following property: if $u$ is a complex-valued unimodular map in $W^{s,p}$, then $u$ has (locally) a phase in $W^{s,p}$.

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Keywords

Sobolev spaces, Ginzburg-Landau functional, problems of the Ginzburg-Landau type, unimodular maps, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, lifting, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], lifting problem

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