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Minimal BV-liftings of W1,1Ω,S1 maps in 2D are “often” unique
Nonlinear Analysis ( IF 1.3 ) Pub Date : 2020-04-30 , DOI: 10.1016/j.na.2020.111943
Eduard Curcă

Let S1 be the unit circle, Ω a smooth, bounded and simply connected domain in R2, and k a positive integer. We prove that the set of configurations a=a1,,akΩk for which each uW1,1Ω,S1C(Ωa1,,ak) admits a unique (mod2π) minimal BV-lifting φBV(Ω,R) is of full measure in Ωk.

In particular, this implies that the set of those uW1,1Ω,S1 that admit a unique (mod2π) minimal BV-lifting is dense in W1,1 Ω,S1. This answers a question of Brezis and Mironescu.



中文翻译:

最小的 BV举重 w ^1个1个Ω小号1个 2D地图“通常”是唯一的

小号1个 是单位圆, Ω 一个光滑,有界且简单连接的域 [R2ķ一个正整数。我们证明了这套配置一种=一种1个一种ķΩķ 对于每个 üw ^1个1个Ω小号1个CΩ一种1个一种ķ 承认一个独特的(Ød2π最小 BV举重 φBVΩ[RΩķ

特别是,这意味着 üw ^1个1个Ω小号1个 承认一个独特的(Ød2π最小 BV举重密集 w ^1个1个 Ω小号1个。这回答了布雷齐斯和米罗内斯库的问题。

更新日期:2020-04-30
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