Stability of parabolic Harnack inequalities

Authors:
Martin T. Barlow and Richard F. Bass

Journal:
Trans. Amer. Math. Soc. **356** (2004), 1501-1533

MSC (2000):
Primary 60J27; Secondary 60J35, 31B05

DOI:
https://doi.org/10.1090/S0002-9947-03-03414-7

Published electronically:
September 22, 2003

MathSciNet review:
2034316

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Abstract: Let be a graph with weights for which a parabolic Harnack inequality holds with space-time scaling exponent . Suppose is another set of weights that are comparable to . We prove that this parabolic Harnack inequality also holds for with the weights . We also give stable necessary and sufficient conditions for this parabolic Harnack inequality to hold.

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Additional Information

**Martin T. Barlow**

Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z2

Email:
barlow@math.ubc.ca

**Richard F. Bass**

Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269

Email:
bass@math.uconn.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03414-7

Keywords:
Harnack inequality,
random walks on graphs,
volume doubling,
Green functions,
Poincar\'{e} inequality,
Sobolev inequality,
anomalous diffusion

Received by editor(s):
January 24, 2003

Published electronically:
September 22, 2003

Additional Notes:
The first author’s research was partially supported by an NSERC (Canada) grant, and by CNRS (France)

The second author’s research was partially supported by NSF Grant DMS 9988486

Article copyright:
© Copyright 2003
American Mathematical Society