Abstract.
For each \(g \in BV(S^1,S^1)\), we solve the following variational problem \(E(g)=\inf \left\{ \int_{S^1} |\dot{\varphi}| \, :\, \varphi \in BV(S^1, \mathbb{R}), e^{i\varphi}=g \textrm{a.e. on} S^1\right\}\) and we show that \(E(g)\leq 2\vert g\vert _{BV}\).
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Received: 4 November 2003, Accepted: 10 May 2004, Published online: 16 July 2004
Radu Ignat: Radu.Ignat@ens.fr
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Ignat, R. Optimal lifting for BV(S 1,S 1). Calc. Var. 23, 83–96 (2005). https://doi.org/10.1007/s00526-004-0291-8
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DOI: https://doi.org/10.1007/s00526-004-0291-8