Martin boundary of a fractal domain

被引：16

作者：

Aikawa, H ^{[1
]}

Lundh, T

Mizutani, T

机构：

[1] Shimane Univ, Dept Math, Matsue, Shimane 6908504, Japan

[2] Chalmers Univ Technol, Dept Math, S-41296 Gothenburg, Sweden

[3] Hiroshima Univ, Dept Math, Higashihiroshima 7398526, Japan

[4] Mittag Leffler Inst, Djursholm, Sweden

来源：

POTENTIAL ANALYSIS | 2003年 / 18卷 / 04期

关键词：

Martin boundary; fractal; boundary Harnack principle; Green function; uniformly John domain; internal metric;

D O I：

10.1023/A:1021823023212

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A uniformly John domain is a domain intermediate between a John domain and a uniform domain. We determine the Martin boundary of a uniformly John domain D as an application of a boundary Harnack principle. We show that a certain self-similar fractal has its complement as a uniformly John domain. In particular, the complement of the 3-dimensional Sierpinski gasket is a uniform domain and its Martin boundary is homeomorphic to the Sierpinski gasket itself.

引用

页码：311 / 357

页数：47

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