The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces

被引：15

作者：

Bjorn, Anders ^{[1
]}

Bjorn, Jana ^{[1
]}

Latvala, Visa ^{[2
]}

机构：

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

[2] Univ Eastern Finland, Dept Phys & Math, POB 111, FI-80101 Joensuu, Finland

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2018年 / 135卷 / 01期

基金：

瑞典研究理事会;

关键词：

P-HARMONIC FUNCTIONS; LIPSCHITZ FUNCTIONS; SUPERHARMONIC FUNCTIONS; SOBOLEV SPACES; CONTINUITY; SETS; QUASICONTINUITY; CONNECTEDNESS; REGULARITY; GRADIENTS;

D O I：

10.1007/s11854-018-0029-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the Cartan and Choquet properties for the fine topology on a complete metric space equipped with a doubling measure supporting a p-Poincar, inequality, 1 < p < a. We apply these key tools to establish a fine version of the Kellogg property, characterize finely continuous functions by means of quasicontinuous functions, and show that capacitary measures associated with Cheeger supersolutions are supported by the fine boundary of the set.

引用

页码：59 / 83

页数：25