Indecomposable sets of finite perimeter in doubling metric measure spaces

被引：6

作者：

Bonicatto, Paolo ^{[1
]}

Pasqualetto, Enrico ^{[2
]}

Rajala, Tapio ^{[2
]}

机构：

[1] Univ Basel, Dept Math & Informat, Spiegelgasse 1, CH-4051 Basel, Switzerland

[2] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, Jyvaskyla 40014, Finland

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 59卷 / 02期

基金：

芬兰科学院;

关键词：

26B30; 53C23; FINE PROPERTIES; INEQUALITIES; RELAXATION;

D O I：

10.1007/s00526-020-1725-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak (1,1)-Poincare inequality. The two main results we obtain are a decomposition theorem into indecomposable sets and a characterisation of extreme points in the space of BV functions. In both cases, the proof we propose requires an additional assumption on the space, which is called isotropicity and concerns the Hausdorff-type representation of the perimeter measure.

引用

页数：39

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