cvgmt: An overview of regularity results for the Laplacian and $p$-Laplacian in metric spaces

Calculus of Variations and Geometric Measure Theory

I. Y. Violo

An overview of regularity results for the Laplacian and $p$-Laplacian in metric spaces

created by violo on 05 Dec 2025

[BibTeX]

Published Paper

Inserted: 5 dec 2025
Last Updated: 5 dec 2025

Journal: Indag. Math.
Year: 2025

Abstract:

We review some regularity results for the Laplacian and $p$-Laplacian in metric measure spaces. The focus is mainly on interior Hölder, Lipschitz and second-regularity estimates and on spaces supporting a Poincaré inequality or having Ricci curvature bounded below.