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arXiv:2502.00825 [math.AP]AbstractReferencesReviewsResources

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

Ivan Yuri Violo

Published 2025-02-02Version 1

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

Categories: math.AP, math.MG
Subjects: 35B65, 35J92, 46E36, 58J05
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