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Coupling and Harnack inequalities for Sierpiński carpets
Author(s):
Martin T.
Barlow;
Richard F.
Bass
Journal:
Bull. Amer. Math. Soc.
29
(1993),
208-212.
MSC (2000):
Primary 60B99;
Secondary 28A80, 60J35
MathSciNet review:
1215306
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Additional information
Abstract:
Uniform Harnack inequalities for harmonic functions on the pre-and graphical Sierpinski carpets are proved using a probabilistic coupling argument. Various results follow from this, including the construction of Brownian motion on Sierpinski carpets embedded in  ,  , estimates on the fundamental solution of the heat equation, and Sobolev and Poincaré inequalities.
References:
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- M. T. Barlow and R. F. Bass, The construction of Brownian motion on the Sierpinski carpet, Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), 225-257. MR 1023950 (91d:60183)
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Additional Information:
DOI:
10.1090/S0273-0979-1993-00424-5
PII:
S 0273-0979(1993)00424-5
Keywords:
Harnack inequality,
Sierpinski carpets,
self-similar,
fractals,
Brownian motion,
heat equation,
transition densities,
Poincaré inequality,
Sobolev inequality,
spectral dimension,
electrical resistance
Copyright of article:
Copyright
1993,
American Mathematical Society
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