The annular decay property and capacity estimates for thin annuli

被引：10

作者：

Bjorn, Anders ^{[1
]}

Bjorn, Jana ^{[1
]}

Lehrback, Juha ^{[2
]}

机构：

[1] Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden

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

来源：

COLLECTANEA MATHEMATICA | 2017年 / 68卷 / 02期

基金：

芬兰科学院; 瑞典研究理事会;

关键词：

Annular decay property; Capacity; Doubling measure; Metric space; Newtonian space; Poincare inequality; Sobolev space; Thin annulus; Upper gradient; Variational capacity; Weighted R-n; SPACES; INEQUALITIES;

D O I：

10.1007/s13348-016-0178-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted and in metric spaces, primarily under the assumptions of an annular decay property and a Poincar, inequality. In particular, if the measure has the 1-annular decay property at and the metric space supports a pointwise 1-Poincar, inequality at , then the upper and lower bounds are comparable and we get a two-sided estimate for thin annuli centred at . This generalizes the known estimate for the usual variational capacity in unweighted . We also characterize the 1-annular decay property and provide examples which illustrate the sharpness of our results.

引用

页码：229 / 241

页数：13

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