Domains of Dirichlet forms and effective resistance estimates on p.c.f. fractals

被引：15

作者：

Hu, Jiaxin ^{[1
]}

Wang, Xingsheng

机构：

[1] Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Univ Glasgow, Dept Elect & Elect Engn, Glasgow G12 8QQ, Lanark, Scotland

来源：

STUDIA MATHEMATICA | 2006年 / 177卷 / 02期

关键词：

p.c.f; fractal; Dirichlet form; effective resistance; partition; domain; Sobolev-type space;

D O I：

10.4064/sm177-2-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider post-critically finite self-similar fractals with regular harmonic structures. We first obtain effective resistance estimates in terms of the Euclidean metric, which in particular imply the embedding theorem for the domains of the Dirichlet forms associated with the harmonic structures. We then characterize the domains of the Dirichlet forms.

引用

页码：153 / 172

页数：20

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