Sobolev space properties of superharmonic functions on metric spaces

被引：4
|
作者：
Juha Kinnunen
Olli Martio
机构：
[1] Helsinki University of Technology,K., Institute of Mathematics
[2] University of Helsinki,O.M., Department of Mathematics
来源：
Results in Mathematics | 2003年 / 44卷 / 1-2期
关键词：
31C45; 46E35;
D O I：
10.1007/BF03322918
中图分类号：
学科分类号：
摘要：
Our objective is to study regularity of superharmonic functions of a nonlinear potential theory on metric measure spaces. In particular, we are interested in the local integrability properties of a superharmonic function and its derivative. We show that every superharmonic function has a weak upper gradient and provide sharp local integrability estimates. In addition, we study absolute continuity of a superharmonic function.
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页码：114 / 129
页数：15
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