Weyl's lemma on $RCD(K,N)$ metric measure spaces
Differential Geometry
2022-12-20 v1 Analysis of PDEs
Metric Geometry
Abstract
In this paper, we extend the classical Weyl's lemma to metric measure spaces. As its applications, we show the local regularity of solutions for Poisson equations and a Liouville-type result for very weak harmonic functions on spaces. Meanwhile, a byproduct is that we obtain a gradient estimate for solutions to a class of elliptic equations with dis-continuous coefficients.
Keywords
Cite
@article{arxiv.2212.09022,
title = {Weyl's lemma on $RCD(K,N)$ metric measure spaces},
author = {Yu Peng and Hui-Chun Zhang and Xi-Ping Zhu},
journal= {arXiv preprint arXiv:2212.09022},
year = {2022}
}
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21 pages