Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale

Kari Astala; Martí Prats; Eero Saksman

doi:10.1016/j.matpur.2024.04.008

Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale

Kari Astala, Martí Prats, Eero Saksman

Departament de Matemàtiques

University of Helsinki

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Resum

We study quasiconformal mappings in planar domains Ω and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary ∂Ω and of the smoothness of the Beltrami coefficient, that guarantee the global regularity of the mappings in these classes. In the Triebel-Lizorkin class with smoothness below 1, the same conditions give global regularity in Ω for the principal solutions with Beltrami coefficient supported in Ω.

Idioma original	Anglès
Pàgines (de-a)	205-250
Nombre de pàgines	46
Revista	Journal des Mathematiques Pures et Appliquees
Volum	186
DOIs	https://doi.org/10.1016/j.matpur.2024.04.008
Estat de la publicació	Publicada - de juny 2024

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10.1016/j.matpur.2024.04.008Llicència: Creative Commons Reconeixement No Comercial - Sense Obra Derivada

https://ddd.uab.cat/record/293845

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INTEGRALES SINGULARES, TEORIA GEOMETRICA DE LA MEDIDA Y EDP'S
Tolsa Domenech, X. (Investigador/a principal), Dabrowski ., D. M. (Col.laborador/a), Gallegos Saliner, J. M. (Col.laborador/a), Guillen Mola, I. (Col.laborador/a), Molero Casanova, A. (Col.laborador/a), Prats Soler, M. (Col.laborador/a), Sakellaris , G. (Col.laborador/a), Martin Pedret, J. (Investigador/a), Prat Baiget, L. (Investigador/a), Hernandez Garcia, J. (Col.laborador/a) & Ville Oikari, T. (Col.laborador/a)
1/09/21 → 31/08/25
Projecte: Projectes i Ajuts a la Recerca

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title = "Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale",

abstract = "We study quasiconformal mappings in planar domains Ω and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary ∂Ω and of the smoothness of the Beltrami coefficient, that guarantee the global regularity of the mappings in these classes. In the Triebel-Lizorkin class with smoothness below 1, the same conditions give global regularity in Ω for the principal solutions with Beltrami coefficient supported in Ω.",

keywords = "Quasiconformal, Sobolev, Triebel-Lizorkin, Beltrami",

author = "Kari Astala and Mart{\'i} Prats and Eero Saksman",

note = "Publisher Copyright: {\textcopyright} 2024 The Authors",

year = "2024",

month = jun,

doi = "10.1016/j.matpur.2024.04.008",

language = "English",

volume = "186",

pages = "205--250",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

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TY - JOUR

T1 - Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale

AU - Astala, Kari

AU - Prats, Martí

AU - Saksman, Eero

PY - 2024/6

Y1 - 2024/6

N2 - We study quasiconformal mappings in planar domains Ω and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary ∂Ω and of the smoothness of the Beltrami coefficient, that guarantee the global regularity of the mappings in these classes. In the Triebel-Lizorkin class with smoothness below 1, the same conditions give global regularity in Ω for the principal solutions with Beltrami coefficient supported in Ω.

AB - We study quasiconformal mappings in planar domains Ω and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary ∂Ω and of the smoothness of the Beltrami coefficient, that guarantee the global regularity of the mappings in these classes. In the Triebel-Lizorkin class with smoothness below 1, the same conditions give global regularity in Ω for the principal solutions with Beltrami coefficient supported in Ω.

KW - Quasiconformal

KW - Sobolev

KW - Triebel-Lizorkin

KW - Beltrami

UR - https://www.scopus.com/pages/publications/85193551955

UR - https://www.mendeley.com/catalogue/bd9b04c8-580b-3f46-9067-80890ba3eff6/

U2 - 10.1016/j.matpur.2024.04.008

DO - 10.1016/j.matpur.2024.04.008

M3 - Article

SN - 0021-7824

VL - 186

SP - 205

EP - 250

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale

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