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Second-order estimates for the $p$-Laplacian in RCD spaces

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arxiv 2401.09982 v2 pith:DZEUN4L5 submitted 2024-01-18 math.MG math.APmath.DG

Luca Benatti , Ivan Yuri Violo This is my paper · ORCID
classification math.MGmath.APmath.DG
keywords laplacianfunctionshavingintegrableregularitysecond-orderspacesassumption
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abstract

We establish quantitative second-order Sobolev regularity for functions having a $2$-integrable $p$-Laplacian in bounded RCD spaces, with $p$ in a suitable range. In the finite-dimensional case, we also obtain Lipschitz regularity under the assumption that $p$-Laplacian is sufficiently integrable. Our results cover both $p$-Laplacian eigenfunctions and $p$-harmonic functions having relatively compact level sets.

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  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.

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