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

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 L 1 very weak harmonic functions on RCD ( K ,  N ) spaces. Meanwhile, as an application of...

Full description

Saved in:
Bibliographic Details
Published in:Calculus of variations and partial differential equations 2025, Vol.64 (1), Article 5
Main Authors: Peng, Yu, Zhang, Hui-Chun, Zhu, Xi-Ping
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Elliptic functions
Harmonic functions
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Poisson equation
Regularity
Systems Theory
Theoretical
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 L 1 very weak harmonic functions on RCD ( K ,  N ) spaces. Meanwhile, as an application of regularity theory on non-smooth settings, we obtain a gradient estimate for solutions to a class of elliptic equations with discontinuous coefficients.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-024-02862-x