Bi-Sobolev Extensions
Abstract
We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal variant of the famous Beurling–Ahlfors extension theorem is obtained. Furthermore we show that the existing extension techniques such as applying either the harmonic or the Beurling–Ahlfors operator work poorly in the degenerated setting. This also gives an affirmative answer to a question of Karafyllia and Ntalampekos.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202307104467Use this for linking
Review status
Peer reviewed
ISSN
1050-6926
DOI
https://doi.org/10.1007/s12220-023-01363-1
Language
English
Published in
Journal of Geometric Analysis
Citation
- Koski, A., & Onninen, J. (2023). Bi-Sobolev Extensions. Journal of Geometric Analysis, 33(9), Article 301. https://doi.org/10.1007/s12220-023-01363-1
License
Additional information about funding
Open Access funding provided by Aalto University.
Copyright© The Author(s) 2023