Martin boundary of a fractal domain
Artikel i vetenskaplig tidskrift, 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

Författare

Hiroaki Aikawa

Shimane University

Torbjörn Lundh

Göteborgs universitet

Chalmers, Institutionen för matematik

Tomohiko Mizutani

Hiroshima University

Potential Analysis

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

Vol. 18 4 311-357

Ämneskategorier

Matematisk analys

DOI

10.1023/a:1021823023212

Mer information

Senast uppdaterat

2023-08-21