Martin Boundary of a Fractal Domain

被引：0
|
作者：
Hiroaki Aikawa
Torbjörn Lundh
Tomohiko Mizutani
机构：
[1] Shimane University,Department of Mathematics
[2] Chalmers University of Technology,Department of Mathematics
[3] Hiroshima University,Department of Mathematics
来源：
Potential Analysis | 2003年 / 18卷
关键词：
Martin boundary; fractal; boundary Harnack principle; Green function; uniformly John domain; internal metric;
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学科分类号：
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 Sierpiński gasket is a uniform domain and its Martin boundary is homeomorphic to the Sierpiński gasket itself.
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页码：311 / 357
页数：46
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