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arXiv · 2212.09022

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

Yu Peng·Hui-Chun Zhang·Xi-Ping Zhu
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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 $L^1$ 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.

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BibTeXRIS

Yu Peng, Hui-Chun Zhang, Xi-Ping Zhu. 2022-12-18. Weyl's lemma on $RCD(K,N)$ metric measure spaces. https://arxiv.org/abs/2212.09022

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