Gradient vector fields with values into $ {S}^{1}$

Radu Ignat

doi:10.1016/j.crma.2011.07.024

Partial Differential Equations/Functional Analysis

Gradient vector fields with values into

S^{1}

Presented by: Haïm Brezis

Radu Ignat ¹

¹ Laboratoire de Mathématiques, Université Paris-Sud 11, Bât. 425, 91405 Orsay cedex, France

Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 883-887.

Abstract
Résumé

We state the following regularity result: if a two-dimensional gradient vector field $v = \nabla ψ$ with values into the unit circle $S^{1}$ belongs to $H^{1 / 2}$ (or $W^{1, 1}$ ) 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 $v = \nabla ψ$ est à valeurs dans le cercle unité $S^{1}$ et appartient à $H^{1 / 2}$ (ou $W^{1, 1}$ ) 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.

Received: 2011-04-18
Accepted: 2011-07-28
Published online: 2011-08-01

DOI: 10.1016/j.crma.2011.07.024

Author's affiliations:

Radu Ignat ¹

¹ Laboratoire de Mathématiques, Université Paris-Sud 11, Bât. 425, 91405 Orsay cedex, France

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     title = {Gradient vector fields with values into $ {S}^{1}$},
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Radu Ignat. Gradient vector fields with values into $ {S}^{1}$. Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 883-887. doi : 10.1016/j.crma.2011.07.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.07.024/

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