Stability of parabolic Harnack inequalities on metric measure spaces
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- Barlow Martin T.
- Department of Mathematics, University of British Columbia
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- Bass Richard F.
- Department of Mathematics, University of Connecticut
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- Kumagai Takashi
- Research Institute for Mathematical Sciences, Kyoto University
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Abstract
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.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 58 (2), 485-519, 2006
The Mathematical Society of Japan
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Keywords
Details 詳細情報について
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- CRID
- 1390282680093225984
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- NII Article ID
- 10018381344
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- MRID
- 2228569
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- NDL BIB ID
- 7892140
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed