Pith. sign in

REVIEW 1 cited by

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2212.09022 v1 pith:HWUAHZMM submitted 2022-12-18 math.DG math.APmath.MG

Yu Peng , Hui-Chun Zhang , Xi-Ping Zhu This is my paper · ORCID
classification math.DGmath.APmath.MG
keywords spacesequationslemmameasuremetricsolutionsweylapplications
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An overview of regularity results for the Laplacian and $p$-Laplacian in metric spaces

    math.AP 2025-02 conditional novelty 2.0 of 10

    A survey of regularity estimates for the Laplacian and p-Laplacian on metric measure spaces, with a proof overview of the author's second-order regularity theorem in bounded RCD spaces.

Pith tools