Martin boundary of a fractal domain
Journal article, 2003

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 Sierpinacuteski gasket is a uniform domain and its Martin boundary is homeomorphic to the Sierpinacuteski gasket itself.

uniformly John domain

Martin boundary

internal metric

Green function

fractal

boundary Harnack principle

Author

Hiroaki Aikawa

Shimane University

Torbjörn Lundh

University of Gothenburg

Chalmers, Department of Mathematics

Tomohiko Mizutani

Hiroshima University

Potential Analysis

0926-2601 (ISSN) 1572-929X (eISSN)

Vol. 18 4 311-357

Subject Categories

Mathematical Analysis

DOI

10.1023/a:1021823023212

More information

Latest update

8/21/2023