Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)


Coupling and Harnack inequalities for Sierpiński carpets

Authors: Martin T. Barlow and Richard F. Bass
Journal: Bull. Amer. Math. Soc. 29 (1993), 208-212
MSC (2000): Primary 60B99; Secondary 28A80, 60J35
MathSciNet review: 1215306
Full-text PDF

Abstract | References | Similar Articles | 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 $ {\mathbb{R}^d}$, $ d \geq 3$, estimates on the fundamental solution of the heat equation, and Sobolev and Poincaré inequalities.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 60B99, 28A80, 60J35

Retrieve articles in all journals with MSC (2000): 60B99, 28A80, 60J35

Additional Information

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
Article copyright: © Copyright 1993 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia