Weyl's lemma on RCD(K,N) metric measure spaces

2022/12/18 by Peng Yu, Peng, Yu, Hui-Chun Zhang +3 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.09022

openalex publication_date 2022/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend the classical Weyl's lemma to RCD(K,N) metric measure spaces. As its applications, we show the local regularity of solutions for Poisson equations and a Liouville-type result for L¹ very weak harmonic functions on RCD(K,N) spaces. Meanwhile, a byproduct is that we obtain a gradient estimate for solutions to a class of elliptic equations with dis-continuous coefficients.

Cited by

• Optimal boundary regularity of harmonic maps from RCD(K,N)-spaces to CAT(0)-spaces

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