Abstract

We show that for every u ? BV(?; S1), there exists a bounded variation function ? ? BV(?; ?) such that u = ei? a.e. on ? and ? BV ? 2 u BV. The constant 2 is optimal in dimension n > 1. © 2003 Académie des sciences. Published by Éditions scientifiques et médicales Elsevier SAS. All rights reserved.