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

Luca Benatti; Ivan Yuri Violo

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

Metric Geometry 2025-05-23 v2 Analysis of PDEs Differential Geometry

Authors: Luca Benatti , Ivan Yuri Violo

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.

Keywords

sobolev spaces harmonic functions laplacian eigenfunctions

Cite

@article{arxiv.2401.09982,
  title  = {Second-order estimates for the $p$-Laplacian in RCD spaces},
  author = {Luca Benatti and Ivan Yuri Violo},
  journal= {arXiv preprint arXiv:2401.09982},
  year   = {2025}
}

Comments

Minor corrections, published version in JDE (doi:10.1016/j.jde.2025.113398). Comments are welcome!

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