Published Paper

Inserted: 19 jan 2024
Last Updated: 13 aug 2025

Journal: Journal of Differential Equations
Year: 2025
Doi: https://doi.org/10.1016/j.jde.2025.113398

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.