Abstract
The aim of this note is to summarise some of the approaches to extending Sobolev space theory to metric measure spaces. In particular, we will give a brief survey of Hajłasz-Sobolev, Newton-Sobolev, and the Korevaar-Schoen type Sobolev spaces on metric measure spaces.
Information
Published: 1 January 2006
First available in Project Euclid: 16 December 2018
zbMATH: 1120.31004
MathSciNet: MR2277824
Digital Object Identifier: 10.2969/aspm/04410077
Subjects:
Primary:
31C45
Keywords:
metric measure spaces
,
Newtonian space
,
Poincaré inequality
,
upper gradients
Rights: Copyright © 2006 Mathematical Society of Japan
