[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.
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@article{CRMATH_2003__337_3_159_0,
author = {D\'avila, Juan and Ignat, Radu},
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},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00314-5/}
}
TY - JOUR AU - Dávila, Juan AU - Ignat, Radu TI - Lifting of BV functions with values in S1 JO - Comptes Rendus. Mathématique PY - 2003 SP - 159 EP - 164 VL - 337 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00314-5/ DO - 10.1016/S1631-073X(03)00314-5 LA - en ID - CRMATH_2003__337_3_159_0 ER -
%0 Journal Article %A Dávila, Juan %A Ignat, Radu %T Lifting of BV functions with values in S1 %J Comptes Rendus. Mathématique %D 2003 %P 159-164 %V 337 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00314-5/ %R 10.1016/S1631-073X(03)00314-5 %G en %F CRMATH_2003__337_3_159_0
Dávila, Juan; Ignat, Radu. Lifting of BV functions with values in S1. Comptes Rendus. Mathématique, Tome 337 (2003) no. 3, pp. 159-164. doi : 10.1016/S1631-073X(03)00314-5. http://www.numdam.org/articles/10.1016/S1631-073X(03)00314-5/
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