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

2025/02/02 by Violo, Ivan Yuri · 3 citations
#35B65 #35J92 #46E36 #58J05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2502.00825

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.

Cited by

• Regularity for quasilinear elliptic equations in metric measure spaces
• Mean curvature and sharp Willmore inequalities in metric spaces
• A new characterization of Sobolev spaces on Lipschitz differentiability spaces

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