通过公设空间中的周长最小化用 BV 扩展集进行逼近

IF 0.9 2区 数学 Q2 MATHEMATICS
Jesse Koivu, Danka Lučić, Tapio Rajala
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引用次数: 0

摘要

我们证明,公度量空间中的每个有界域都可以用封闭的 $BV$ 扩展集从内部逼近度量。扩展集是通过最小化域与集之间的周长之和与差的度量而得到的。根据早先的结果,在 PI 空间中,最小化集具有局部准最小曲面的开放代表。我们给出了一个 PI 空间的例子,说明最小化的开放代表不一定是 $BV$ 扩展域,也不一定是局部约翰。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximation by BV-extension Sets via Perimeter Minimization in Metric Spaces
We show that every bounded domain in a metric measure space can be approximated in measure from inside by closed $BV$-extension sets. The extension sets are obtained by minimizing the sum of the perimeter and the measure of the difference between the domain and the set. By earlier results, in PI spaces the minimizers have open representatives with locally quasiminimal surface. We give an example in a PI space showing that the open representative of the minimizer need not be a $BV$-extension domain nor locally John.
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来源期刊
CiteScore
2.00
自引率
10.00%
发文量
316
审稿时长
1 months
期刊介绍: International Mathematics Research Notices provides very fast publication of research articles of high current interest in all areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.
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