Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
type: Item
instance of: scholarly article
title: Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
zbMATH Open document ID: 0974.46038
DOI: 10.4171/RMI/275
author: Nageswari Shanmugalingam
published in: Revista Matemática Iberoamericana
publication date: 2001-05-13T00:00:00Z
full work available at URL: https://eudml.org/doc/39609
review text: The author studies a possible definition of Sobolev spaces in abstract metric spaces, and answers in the affirmative the question whether this definition yields a Banach space. The author also explores the relationship between this definition and the Sobolev spaces defined by Hajłasz. For specialized metric spaces, the Sobolev embedding theorems are established. Different versions of capacities are also explored, and these various definitions are compared. The main tool used in this paper is the concept of moduli of path families.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 1563249
zbMATH Keywords: Sobolev space
zbMATH Keywords: metric measure space
zbMATH Keywords: doubling space
zbMATH Keywords: gradient
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: embedding theorem
zbMATH Keywords: capacity
zbMATH Keywords: path family
reviewed by: Dachun Yang
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1563249