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

boundary Harnack principle

internal metric

Green function

fractal

Martin boundary

Författare

Torbjörn Lundh

Chalmers, Institutionen för matematik

Göteborgs universitet

Tomohiko Mizutani

Potential Analysis

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

Vol. 18 311-357

Ämneskategorier

Matematisk analys