A Note on Lipschitz Continuity of Solutions of Poisson Equations in Metric Measure Spaces

Martin Kell

A Note on Lipschitz Continuity of Solutions of Poisson Equations in Metric Measure Spaces

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arxiv 1307.2224 v2 pith:WKGEXO6W submitted 2013-07-08 math.MG math.AP

Martin Kell This is my paper · ORCID

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abstract

In this note we show how to adjust some proofs of Koskela et. al 2003 and Jiang 2011 in order to show that in certain spaces $(X,d,\mu)$, like $RCD(K,N)$-spaces, every Sobolev function with local $L^{p}$-Laplacian and $p>\dim\mu$ is locally Lipschitz continuous.

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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.

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