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.

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.

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.

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. http://www.numdam.org/articles/10.1016/j.crma.2011.07.024/

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