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Martin boundary of a fractal domain

Hiroaki Aikawa ; Torbjörn Lundh (Institutionen för matematik) ; Tomohiko Mizutani
Potential Analysis (0926-2601). Vol. 18 (2003), 4, p. 311-357.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Martin boundary, fractal, boundary Harnack principle, Green function, uniformly John domain, internal metric



Denna post skapades 2006-12-05. Senast ändrad 2014-09-02.
CPL Pubid: 23850

 

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Institutioner (Chalmers)

Institutionen för matematik (2002-2004)

Ämnesområden

Matematisk analys

Chalmers infrastruktur