Uniqueness of lifting and beyond

Haïm Brezis, Petru Mironescu

Research output: Chapter in Book/Report/Conference proceedingChapter


So far, wehave been concerned with the existence of a lifting φ: Ω→ R for a given u: Ω→ S1. A natural question is whether such φ is unique (mod 2 π ). More precisely, assume that we have two liftings, φ1, φ2. Then, φ1(x) - φ2(x) = 2 πk(x) for some k: Ω→ Z. Therefore, we are led to the question of finding minimal assumptions on a measurable function k: Ω→ Z implying that k must be constant. Clearly, continuity is sufficient, but, as we are going to see, constancy holds for a surprisingly large class of functions.

Original languageEnglish (US)
Title of host publicationProgress in Nonlinear Differential Equations and Their Application
Number of pages26
StatePublished - 2021

Publication series

NameProgress in Nonlinear Differential Equations and Their Application
ISSN (Print)1421-1750
ISSN (Electronic)2374-0280

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mechanics
  • Mathematical Physics
  • Control and Optimization
  • Applied Mathematics


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