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

2024/01/18 by Luca Benatti, Benatti, Luca, Ivan Yuri Violo +1 · 1 citation
Mathematics · #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2401.09982

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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• Regularity for quasilinear elliptic equations in metric measure spaces

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