Dimension estimates for the boundary of planar Sobolev extension domains
Abstract
We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev W1,pW1,p -extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Walter de Gruyter GmbH
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202402232106Use this for linking
Review status
Peer reviewed
ISSN
1864-8258
DOI
https://doi.org/10.1515/acv-2021-0042
Language
English
Published in
Advances in Calculus of Variations
Citation
- Lučić, D., Rajala, T., & Takanen, J. (2023). Dimension estimates for the boundary of planar Sobolev extension domains. Advances in Calculus of Variations, 16(2), 517-528. https://doi.org/10.1515/acv-2021-0042
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
All authors partially supported by the Academy of Finland, project 314789.
Copyright© 2023 De Gruyter