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<p>In this paper, we study the discrete Li–Yau gradient estimates for the positive solutions <i>u</i> to the heat equation on graphs under <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(CDE(n,-K)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>C</mi> <mi>D</mi> <mi>E</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mo>-</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> condition and derive a sharper estimate than Bauer et al. (J. Differ. Geom. <b>99</b>(3), 359–405, <CitationRef CitationID="CR1">2015</CitationRef>) and Wang and Zhang (Comm. Anal. Geom. <b>27</b>(4), 969–989, <CitationRef CitationID="CR2">2019</CitationRef>).</p>

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An Improvement on Discrete Li–Yau Inequality

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Bin Shen,
  • Yuhan Zhu

摘要

In this paper, we study the discrete Li–Yau gradient estimates for the positive solutions u to the heat equation on graphs under \(CDE(n,-K)\) C D E ( n , - K ) condition and derive a sharper estimate than Bauer et al. (J. Differ. Geom. 99(3), 359–405, 2015) and Wang and Zhang (Comm. Anal. Geom. 27(4), 969–989, 2019).