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<p>We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for Hölder or even Lipschitz continuity of the kernels. We apply our results to (pseudo)differential operators on domains and metric graphs, to Laplacians on a class of fractals including the Sierpiński gasket, and to structurally damped wave equations. An extension to non-autonomous problems is also discussed.</p>

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On the Lipschitz continuity of the heat kernel

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月15日

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  • Patrizio Bifulco,
  • Delio Mugnolo

摘要

We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for Hölder or even Lipschitz continuity of the kernels. We apply our results to (pseudo)differential operators on domains and metric graphs, to Laplacians on a class of fractals including the Sierpiński gasket, and to structurally damped wave equations. An extension to non-autonomous problems is also discussed.