The BV-capacity in metric spaces
The BV-capacity in metric spaces
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DOI：
10.1007/s00229-010-0337-5
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发表时间：
2010-02
影响因子：
0.6
通讯作者：
H. Hakkarainen;J. Kinnunen
中科院分区：
文献类型：
--
作者：
H. Hakkarainen;J. Kinnunen
研究了具有双测度且支持弱poincarcarve不等式的完备度量空间中1阶的bv容量和Sobolev容量的基本性质。特别地，我们证明了bv -容量是Choquet容量，而Sobolev - 1容量不是。然而，这些量与双侧估计是相等的，并且它们具有与余维1的豪斯多夫度量相同的零集。有界变分函数理论在我们的论证中起着重要的作用。主要工具是拳击不等式的修改版本。
We study basic properties of the BV-capacity and Sobolev capacity of order one in a complete metric space equipped with a doubling measure and supporting a weak Poincaré inequality. In particular, we show that the BV-capacity is a Choquet capacity and the Sobolev 1-capacity is not. However, these quantities are equivalent by two sided estimates and they have the same null sets as the Hausdorff measure of codimension one. The theory of functions of bounded variation plays an essential role in our arguments. The main tool is a modified version of the boxing inequality.