Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces
type: Item
instance of: scholarly article
title: Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces
zbMATH Open document ID: 1027.31006
DOI: 10.1016/S0022-1236(02)00090-3
author: Kai Rajala
author: Nageswari Shanmugalingam
author: Pekka Koskela
published in: Journal of Functional Analysis
publication date: 2003-09-04T00:00:00Z
review text: Lipschitz continuity of Cheeger-harmonic functions in certain metric spaces is established by means of properties of the heat kernel. The metric spaces under consideration are those endowed with a doubling measure supporting a \((1,2)\)-Poincaré inequality and the corresponding Sobolev-Poincaré type inequality for the modification of the measure obtained via the heat kernel. Sharp examples are also provided showing that in the general settings the best possible regularity for the Cheeger-harmonic functions is the Lipschitz one.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 31C05
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1974794
zbMATH Keywords: Cheeger-harmonic
zbMATH Keywords: Lipschitz continuity
zbMATH Keywords: doubling measure
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: hypercontractivity
zbMATH Keywords: logarithmic Sobolev inequality
zbMATH Keywords: Newtonian space
zbMATH Keywords: heat kernel
Wikidata QID: Q109994536
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1974794