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Heat kernel estimates and related inequalities on metric graphs

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arxiv 1101.3010 v1 pith:3X3QGA7R submitted 2011-01-15 math-ph math.MP

Sebastian Haeseler This is my paper · ORCID
classification math-phmath.MP
keywords metricestimatesgraphsheatinequalitiesinequalitykernelrelated
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We consider metric graphs with Kirchhoff boundary conditions. We study the intrinsic metric, volume doubling and a Poincar\'e inequality. This enables us to prove a parabolic Harnack inequality. The proof involves various techniques from the theory of strongly local Dirichlet forms. Along our way we show Sobolev and Nash type inequalities and related heat kernel estimates.

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  1. On the heat content of compact quantum graphs

    math.SP 2025-02 conditional novelty 7.0 of 10

    For compact metric graphs with Dirichlet conditions, the heat content is shown to equal the volume minus a boundary term plus a weighted sum over Dirichlet-to-Dirichlet paths, for all positive times.

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