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

@inproceedings{Bourgain2000OnTS,
  title={On the structure of the Sobolev space H1/2 with values into the circle},
  author={Jean Bourgain and Haim Brezis and Petru Mironescu},
  year={2000}
}
Abstract We are concerned with properties of H 1/2 (Ω; S 1 ) where Ω is the boundary of a domain in R 3 . To every u∈ H 1/2 (Ω; S 1 ) 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; S 1 ) in H 1/2 coincides with the u 's such that T ( u )=0. Moreover, every u ∈ Y admits a unique ( mod . 2π) lifting in H 1/2 +W 1,1 . We also discuss an application to the 3-d Ginzburg–Landau problem. 

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