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 language||English (US)|
|Number of pages||6|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|State||Published - Jul 15 2000|
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