Discrete versions of the Li-Yau gradient estimate

• Dominik Dier ^[1] ; Moritz Kassmann ^[2] ; Rico Zacher ^[1]
  1. [1] University of Ulm

     University of Ulm

     Stadtkreis Ulm, Alemania

     
  2. [2] Fakultät für Mathematik Postfach, Germany
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 22, Nº 2, 2021, págs. 691-744
• Idioma: inglés
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• Resumen

  • We study positive solutions to the heat equation on graphs. We prove variants of the Li-Yau gradient estimate and the differential Harnack inequality.

    For some graphs, we can show the estimates to be sharp. We establish new com- putation rules for differential operators on discrete spaces and introduce a re- laxation function that governs the time dependency in the differential Harnack estimate