University of Oulu

Hästö, P., Ribeiro, A. (2017) Characterization of the variable exponent Sobolev norm without derivatives. Communications in Contemporary Mathematics, 19 (03), 1650022. doi:10.1142/S021919971650022X

Characterization of the variable exponent Sobolev norm without derivatives

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Author: Hästö, Peter1,2; Ribeiro, Ana Margarida3,4
Organizations: 1Department of Mathematical Sciences, University of Oulu
2Department of Mathematics and Statistics, University of Turku, Finland
3Centro de Matemática e Aplicações (CMA), Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa
4Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.1 MB)
Persistent link: http://urn.fi/urn:nbn:fi-fe2019040110638
Language: English
Published: World Scientific, 2017
Publish Date: 2016-03-30
Description:

Abstract

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Since the difference quotient is based on shifting the function, it cannot be generalized to the variable exponent case. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the variable exponent Sobolev space.

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Series: Communications in contemporary mathematics
ISSN: 0219-1997
ISSN-E: 0219-1997
ISSN-L: 0219-1997
Volume: 19
Issue: 3
Article number: 1650022
DOI: 10.1142/S021919971650022X
OADOI: https://oadoi.org/10.1142/S021919971650022X
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Subjects:
Copyright information: Electronic version of an article published as Communications in Contemporary Mathematics, 19, 03, 2017, https://doi.org/10.1142/S021919971650022X © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ccm.