Stability of parabolic Harnack inequalities on metric measure spaces

• Barlow Martin T.

  Department of Mathematics, University of British Columbia

• Bass Richard F.

  Department of Mathematics, University of Connecticut

• Kumagai Takashi

  Research Institute for Mathematical Sciences, Kyoto University

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

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 58 (2), 485-519, 2006

  The Mathematical Society of Japan

Keywords

• Harnack inequality
• volume doubling
• Green functions
• Poincaré inequality
• Sobolev inequality
• rough isometry
• anomalous diffusion

Details

• CRID: 1390282680093225984
• NII Article ID: 10018381344
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/1149166785
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2228569
• NDL BIB ID: 7892140
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7892140
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed