The Hölder regularity of harmonic function on bounded and unbounded p.c.f self-similar sets

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Jin Gao, Yijun Song
DOI: 10.48550/arxiv.2603.00659
Cited by: 0
References: 1

Abstract

In this paper, we prove a generalized reverse Hölder inequality of harmonic functions on cable systems induced by post-critically finite (p.c.f.) self-similar sets. Furthermore, we also establish the Hölder regularity of harmonic functions on both bounded and unbounded p.c.f. self-similar sets, which does not involve heat kernel estimates and resistance estimates.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Mathematical Dynamics and Fractals Stochastic processes and statistical mechanics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
28 February 2026
Language
EN
Document type
Preprint