Bi-Sobolev Extensions

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2023-09

Department

Department of Mathematics and Systems Analysis

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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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DOI

10.1007/s12220-023-01363-1

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

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https://urn.fi/URN:NBN:fi:aalto-202308114750

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[article-cris] Perustieteiden korkeakoulu / SCI