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Gaussian bounds and parabolic Harnack inequality on locally irregular graphs

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Abstract

A well known theorem of Delmotte is that Gaussian bounds, parabolic Harnack inequality, and the combination of volume doubling and Poincaré inequality are equivalent for graphs. In this paper we consider graphs for which these conditions hold, but only for sufficiently large balls, and prove a similar equivalence.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Martin T. Barlow

  2. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China

    Xinxing Chen

Authors
  1. Martin T. Barlow
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  2. Xinxing Chen
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Correspondence to Xinxing Chen.

Additional information

M. T. Barlow’s research was partially supported by NSERC (Canada). X. Chen’s research was partially supported by China Scholarship Council during the author visiting Department of Mathematics at University of British Columbia in 2012, and NSFC Grant No. 11531001.

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Barlow, M.T., Chen, X. Gaussian bounds and parabolic Harnack inequality on locally irregular graphs. Math. Ann. 366, 1677–1720 (2016). https://doi.org/10.1007/s00208-016-1373-6

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  • DOI: https://doi.org/10.1007/s00208-016-1373-6

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