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April, 2006 Stability of parabolic Harnack inequalities on metric measure spaces
Martin T. BARLOW, Richard F. BASS, Takashi KUMAGAI
J. Math. Soc. Japan 58(2): 485-519 (April, 2006). DOI: 10.2969/jmsj/1149166785


Let ( X , d , μ ) be a metric measure space with a local regular Dirichlet form. We give necessary and sufficient conditions for a parabolic Harnack inequality with global space-time scaling exponent β 2 to hold. We show that this parabolic Harnack inequality is stable under rough isometries. As a consequence, once such a Harnack inequality is established on a metric measure space, then it holds for any uniformly elliptic operator in divergence form on a manifold naturally defined from the graph approximation of the space.


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Martin T. BARLOW. Richard F. BASS. Takashi KUMAGAI. "Stability of parabolic Harnack inequalities on metric measure spaces." J. Math. Soc. Japan 58 (2) 485 - 519, April, 2006.


Published: April, 2006
First available in Project Euclid: 1 June 2006

zbMATH: 1102.60064
MathSciNet: MR2228569
Digital Object Identifier: 10.2969/jmsj/1149166785

Primary: 60J35
Secondary: 31B05 , 31C25

Keywords: Anomalous diffusion , Green functions , Harnack inequality , Poincaré inequality , Rough isometry , Sobolev inequality , volume doubling

Rights: Copyright © 2006 Mathematical Society of Japan


Vol.58 • No. 2 • April, 2006
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