On the structure of the Sobolev space H1/2 with values into the circle

Jean Bourgain, Haïm Brezis, Petru Mironescu

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34 Scopus citations


We are concerned with properties of H1/2(Ω; S1) where Ω is the boundary of a domain in ℝ3. To every u ∈ H1/2(Ω; S1) we associate a distribution T(u) which, in some sense, describes the location and the topological degree of singularities of u. The closure Y of C(Ω; S1) in H1/2 coincides with the u's such that T(u) = 0. Moreover, every u ∈ Y admits a unique (mod. 2π) lifting in H1/2 + W1,1. We also discuss an application to the 3-d Ginzburg-Landau problem.

Original languageEnglish (US)
Pages (from-to)119-124
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Issue number2
StatePublished - Jul 15 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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