Stability of parabolic Harnack inequalities on metric measure spaces

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概要

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• 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.

• 社団法人 日本数学会の論文
• 2006-04-01

著者

• Kumagai Takashi

  Research Institute For Mathematical Sciences Kyoto University

• BARLOW Martin

  Department of Mathematics University of British Columbia

• BASS Richard

  Department of Mathematics University of Connecticut

関連論文

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• Stability of parabolic Harnack inequalities on metric measure spaces
• On the equivalence of parabolic Harnack inequalities and heat kernel estimates
• NASH-TYPE INEQUALITIES AND HEAT KERNELS FOR NON-LOCAL DIRICHLET FORMS
• On the equivalence of parabolic Harnack inequalities and heat kernel estimates

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