[Relèvement des fonctions BV à valeurs sur le cercle S1]
On montre que pour tout , il existe une fonction à variation bornée telle que u=eiϕ 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=eiϕ a.e. on and |ϕ|BV⩽2|u|BV. The constant 2 is optimal in dimension n>1.
Accepté le :
Publié le :
Juan Dávila 1 ; Radu Ignat 2
@article{CRMATH_2003__337_3_159_0,
author = {Juan D\'avila and Radu Ignat},
title = {Lifting of {BV} functions with values in {\protect\emph{S}\protect\textsuperscript{1}}},
journal = {Comptes Rendus. Math\'ematique},
pages = {159--164},
publisher = {Elsevier},
volume = {337},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00314-5},
language = {en},
}
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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