Lifting of BV functions with values in <i>S</i><sup>1</sup>

Juan Dávila; Radu Ignat

doi:10.1016/S1631-073X(03)00314-5

Partial Differential Equations

Lifting of BV functions with values in S¹
[Relèvement des fonctions BV à valeurs sur le cercle S¹]

Présenté par : Haïm Brezis

Juan Dávila ¹ ; Radu Ignat ²

¹ Departamento de Ingenierı́a Matemática, CMM (UMR CNRS), Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile
² École normale supérieure, 45, rue d'Ulm, 75230 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 159-164.

Résumé
Abstract

On montre que pour tout , il existe une fonction à variation bornée telle que u=e^iϕ p.p. dans et |ϕ|_BV⩽2|u|_BV. La constante 2 est optimale en dimension n>1.

We show that for every , there exists a bounded variation function such that u=e^iϕ a.e. on and |ϕ|_BV⩽2|u|_BV. The constant 2 is optimal in dimension n>1.

Reçu le : 2003-06-19
Accepté le : 2003-06-19
Publié le : 2003-07-26

DOI : 10.1016/S1631-073X(03)00314-5

Affiliations des auteurs :

Juan Dávila ¹ ; Radu Ignat ²

¹ Departamento de Ingenierı́a Matemática, CMM (UMR CNRS), Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile
² École normale supérieure, 45, rue d'Ulm, 75230 Paris cedex 05, France

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     author = {Juan D\'avila and Radu Ignat},
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Juan Dávila; Radu Ignat. Lifting of BV functions with values in S¹. Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 159-164. doi : 10.1016/S1631-073X(03)00314-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00314-5/

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