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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
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| 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
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| Publish Date: | 2019-04-01 |
| Description: |
AbstractThe 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. see all
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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. |