Sobolev capacity of the space \(W^{1,p(\cdot)} (\mathbb{R}^n)\)
type: Item
instance of: scholarly article
title: Sobolev capacity of the space \(W^{1,p(\cdot)} (\mathbb{R}^n)\)
zbMATH Open document ID: 1078.46021
DOI: 10.1155/2003/895261
author: Petteri Harjulehto
author: Peter Hästö
author: Mika Koskenoja
author: Susanna Varonen
published in: Journal of Function Spaces and Applications
publication date: 2004-10-28T00:00:00Z
review text: The goal of the authors is to define the notion of Sobolev capacity on the generalized Sobolev space \(W^{1,p(\cdot)}(\mathbb{R}^n)\) and study its properties. They show that the Sobolev \(p(\cdot)\)-capacity is an outer measure and as a corollary they obtain that it is the Choquet capacity. They present several results that illustrate the utility of the Sobolev capacity. Moreover, the authors show that the capacity is related to the Hausdorff dimension. Using quasicontinuous representative in \(W^{1,p(\cdot)}(\mathbb{R}^n)\), the autors derive an estimate of the capacity of level sets of variable exponent Sobolev functions.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 31B15
zbMATH DE Number: 2111351
zbMATH Keywords: Sobolev capacity
zbMATH Keywords: variable exponent
zbMATH Keywords: generalized Sobolev space
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: quasicontinuous representative
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2003/895261
OpenAlex ID: W2036650064
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description: scientific article; zbMATH DE number 2111351