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Martin Boundary of a Fractal Domain |
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| Authors: | Aikawa Hiroaki Lundh Torbjörn Mizutani Tomohiko |
| Institution: | (1) Department of Mathematics, Shimane University, Matsue, 690-8504, Japan;(2) Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden;(3) Department of Mathematics, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan |
| Abstract: | 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 Sierpi ski gasket is a uniform domain and its Martin boundary is homeomorphic to the Sierpiski gasket itself. |
| Keywords: | Martin boundary fractal boundary Harnack principle Green function uniformly John domain internal metric |
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