Bi-Sobolev Extensions

Aleksis Koski; Jani Onninen

doi:10.1007/s12220-023-01363-1

Bi-Sobolev Extensions

Aleksis Koski^*, Jani Onninen

^*Tämän työn vastaava kirjoittaja

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

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Abstrakti

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.

Alkuperäiskieli	Englanti
Artikkeli	301
Sivumäärä	18
Julkaisu	Journal of Geometric Analysis
Vuosikerta	33
Numero	9
DOI - pysyväislinkit	https://doi.org/10.1007/s12220-023-01363-1
Tila	Julkaistu - syysk. 2023
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Pääsy asiakirjaan

10.1007/s12220-023-01363-1Lisenssi: CC BY

SCI_Koski_etal_The_Journal_of_Geometric_Analysis_2023Final published version, 366 KBLisenssi: CC BY

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Linkki julkaisuun Scopuksessa

QUAMAP: Quasiconformal Methods in Analysis and Applications
Astala, K. (Vastuullinen tutkija)
27/08/2019 → 30/04/2021
Projekti: EU: ERC grants

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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.",

keywords = "Beurling–Ahlfors extension, Harmonic extension, Quasiconformal mapping and mapping of finite distortion, Sobolev extensions, Sobolev homeomorphisms",

author = "Aleksis Koski and Jani Onninen",

note = "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: {\textcopyright} 2023, The Author(s). | openaire: EC/H2020/834728/EU//QUAMAP",

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doi = "10.1007/s12220-023-01363-1",

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AU - Koski, Aleksis

AU - Onninen, Jani

N1 - 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

PY - 2023/9

Y1 - 2023/9

N2 - 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.

AB - 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.

KW - Beurling–Ahlfors extension

KW - Harmonic extension

KW - Quasiconformal mapping and mapping of finite distortion

KW - Sobolev extensions

KW - Sobolev homeomorphisms

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U2 - 10.1007/s12220-023-01363-1

DO - 10.1007/s12220-023-01363-1

M3 - Article

AN - SCOPUS:85164323943

SN - 1050-6926

VL - 33

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 9

M1 - 301

ER -

Bi-Sobolev Extensions

Abstrakti

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Muut tiedostot ja linkit

Sormenjälki

Projektit

QUAMAP: Quasiconformal Methods in Analysis and Applications

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