SOBOLEV SPACES, FINE GRADIENTS AND QUASICONTINUITY ON QUASIOPEN SETS

被引：13

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 Math & Phys, POB 111, FI-80101 Joensuu, Finland

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2016年 / 41卷 / 02期

基金：

瑞典研究理事会;

关键词：

Fine gradient; fine topology; metric space; minimal upper gradient; Newtonian space; quasicontinuous; quasiopen; Sobolev space; CONTINUITY;

D O I：

10.5186/aasfm.2016.4130

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space X equipped with a doubling measure supporting a p-Poincare inequality with 1 < p < infinity, and connect them to the Sobolev theory in R-n. In particular, we show that for quasiopen subsets of R-n the Newtonian functions, which are naturally defined in any metric space, coincide with the quasicontinuous representatives of the Sobolev functions studied by Kilpelainen and Maly in 1992.

引用

页码：551 / 560

页数：10

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