The BV-capacity in metric spaces

被引：48

作者：

Hakkarainen, Heikki ^{[2
]}

Kinnunen, Juha ^{[1
]}

机构：

[1] Aalto Univ, Dept Math, Helsinki 02015, Finland

[2] Univ Oulu, Dept Math Sci, Oulu 90014, Finland

来源：

MANUSCRIPTA MATHEMATICA | 2010年 / 132卷 / 1-2期

关键词：

SOBOLEV FUNCTIONS; FINITE PERIMETER; LEBESGUE POINTS; FINE PROPERTIES; INEQUALITY; SETS;

D O I：

10.1007/s00229-010-0337-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Poincare 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.

引用

页码：51 / 73

页数：23

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