Abstract
We show that for every u∈ BV(Ω;S 1) , there exists a bounded variation function ϕ∈ BV(Ω; R) such that u=e i ϕ a.e. on Ω and | ϕ| BV⩽2| u| BV. The constant 2 is optimal in dimension n>1. To cite this article: J. Dávila, R. Ignat, C. R. Acad. Sci. Paris, Ser. I 337 (2003).
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