Comparisons of relative BV-capacities and Sobolev capacity in metric spaces

被引：17

作者：

Hakkarainen, Heikki ^{[1
]}

Shanmugalingam, Nageswari ^{[2
]}

机构：

[1] Univ Oulu, Dept Math Sci, FI-90014 Oulu, Finland

[2] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 16期

关键词：

Capacity; Functions of bounded variation; Sobolev space; Analysis on metric measure spaces; FINITE PERIMETER; FINE PROPERTIES; DERIVATIVES; INEQUALITY; SETS;

D O I：

10.1016/j.na.2011.05.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study relations between the variational Sobolev 1-capacity and versions of variational BV-capacity in a complete metric space equipped with a doubling measure and supporting a weak (1, 1)-Poincare inequality. We prove the equality of 1-modulus and the continuous 1-capacity, extending the known results for 1 < p < infinity to also cover the more geometric case p = 1. Then we give alternative definitions for variational BV-capacities and obtain equivalence results between them. Finally we study relations between total 1-capacity and versions of BV-capacity. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：5525 / 5543

页数：19

共 39 条

[1] Weak differentiability of BV functions on stratified groups [J].