Strong BV-extension and W1,1-extension domains
Abstract
We show that a bounded domain in a Euclidean space is a W1,1-extension domain if and only if it is a strong BV-extension domain. In the planar case, bounded and strong BV-extension domains are shown to be exactly those BV-extension domains for which the set ∂Ω∖⋃iΩ‾i is purely 1-unrectifiable, where Ωi are the open connected components of R2∖Ω‾.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Elsevier
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202208254341Use this for linking
Review status
Peer reviewed
ISSN
0022-1236
DOI
https://doi.org/10.1016/j.jfa.2022.109665
Language
English
Published in
Journal of Functional Analysis
Citation
- García-Bravo, M., & Rajala, T. (2022). Strong BV-extension and W1,1-extension domains. Journal of Functional Analysis, 283(10), Article 109665. https://doi.org/10.1016/j.jfa.2022.109665
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
The authors acknowledge the support from the Academy of Finland, grant no. 314789
Copyright© 2022 The Author(s). Published by Elsevier Inc.