Bi-Sobolev Extensions

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2023-09
Major/Subject
Mcode
Degree programme
Language
en
Pages
18
Series
JOURNAL OF GEOMETRIC ANALYSIS, Volume 33, issue 9
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.
Description
Funding Information: A. Koski was supported by the ERC Advanced Grant number 834728 and by the Finnish Centre of Excellence in Randomness and Structures. J. Onninen was supported by the NSF grant DMS-2154943. Publisher Copyright: © 2023, The Author(s). | openaire: EC/H2020/834728/EU//QUAMAP
Keywords
Beurling–Ahlfors extension, Harmonic extension, Quasiconformal mapping and mapping of finite distortion, Sobolev extensions, Sobolev homeomorphisms
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Citation
Koski , A & Onninen , J 2023 , ' Bi-Sobolev Extensions ' , JOURNAL OF GEOMETRIC ANALYSIS , vol. 33 , no. 9 , 301 . https://doi.org/10.1007/s12220-023-01363-1