Stability of parabolic Harnack inequalities on metric measure spaces

Martin T. Barlow*, Richard F. Bass, Takashi Kumagai

*この研究の対応する著者

研究成果: Article査読

65 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)485-519
ページ数35
ジャーナルJournal of the Mathematical Society of Japan
58
2
DOI
出版ステータスPublished - 2006 4月
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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