Asian Journal of Mathematics

Volume 27 (2023)

Number 5

Off-diagonal lower estimates and Hölder regularity of the heat kernel

Pages: 675 – 770

DOI: https://dx.doi.org/10.4310/AJM.2023.v27.n5.a3

Authors

Alexander Grigor’yan (Fakulät für Mathematik, Universität Bielefeld, Bielefeld, Germany)

Eryan Hu (Center for Applied Mathematics, Tianjin University, Tianjin, China)

Jiaxin Hu (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Abstract

We study the heat kernel of a regular symmetric Dirichlet form on a metric space with doubling measure, in particular, a connection between the properties of the jump measure and the long time behaviour of the heat kernel. Under appropriate optimal hypotheses, we obtain the Hölder regularity and lower estimates of the heat kernel.

Keywords

heat kernel, Dirichlet form, doubling space

2010 Mathematics Subject Classification

Primary 35K08. Secondary 28A80, 60J35.

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Dedicated to the memory of Professor Ka-Sing Lau

The first-named author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 317210226 - SFB 1283, and by the Tsinghua Global Scholars FellowshipProgram.

The second-named was supported by National Key R&D Program of China (No. 2022YFA1006000) and by the National Natural Science Foundation of China (No. 12171354, and No. 11801403).

The third-named author was supported by the National Natural Science Foundation of China (No. 12271282), and by SFB 1283.

Received 30 December 2022

Accepted 10 October 2023

Published 12 July 2024