no. 15-16
Partial Differential Equations/Functional Analysis
Gradient vector fields with values into S1
[Champs de gradient à valeurs dans S1]
Présenté par : Haïm Brezis
Ignat, Radu1
1 Laboratoire de Mathématiques, Université Paris-Sud 11, Bât. 425, 91405 Orsay cedex, France
Comptes Rendus. Mathématique, Tome 349 (2011) no. 15-16, pp. 883-887

We state the following regularity result: if a two-dimensional gradient vector field v=∇ψ with values into the unit circle S1 belongs to H1/2 (or W1,1) then v is locally Lipschitz except at a locally finite number of vortices. We also state approximation results for such vector fields.

Le résultat de régularité suivant a lieu : Si un champ de gradient v=∇ψ est à valeurs dans le cercle unité S1 et appartient à H1/2 (ou W1,1) alors v est localement Lipschitz en dehors dʼun nombre localement fini de points singuliers. Ensuite, des résultats de densité sont énoncés pour cette classe de champs de gradient.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.07.024

Ignat, Radu 1

1 Laboratoire de Mathématiques, Université Paris-Sud 11, Bât. 425, 91405 Orsay cedex, France 
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Ignat, Radu. Gradient vector fields with values into $ {S}^{1}$. Comptes Rendus. Mathématique, Tome 349 (2011) no. 15-16, pp. 883-887. doi: 10.1016/j.crma.2011.07.024

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