Sobolev spaces with zero boundary values on metric spaces

被引：92
作者：
Kilpeläinen, T
Kinnunen, J
Martio, O
机构：
[1] Univ Jyvaskyla, Dept Math, FIN-40351 Jyvaskyla, Finland
[2] Univ Helsinki, Dept Math, FIN-00014 Helsinki, Finland
来源：
POTENTIAL ANALYSIS | 2000年 / 12卷 / 03期
关键词：
capacity; Sobolev spaces;
D O I：
10.1023/A:1008601220456
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We generalize the definition of the first order Sobolev spaces with zero boundary values to an arbitrary metric space endowed with a Borel regular measure. We show that many classical results extend to the metric setting. These include completeness, lattice properties and removable sets.
引用
收藏
页码：233 / 247
页数：15
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