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

Departamento de Matemáticas

University of Helsinki - Helsingin Yliopisto

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

2 Descargas (Pure)

Resumen

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	Inglés
Páginas (desde-hasta)	205-250
Número de páginas	46
Publicación	Journal des Mathematiques Pures et Appliquees
Volumen	186
DOI	https://doi.org/10.1016/j.matpur.2024.04.008
Estado	Publicada - jun 2024

Acceder al documento

10.1016/j.matpur.2024.04.008Licencia: CC BY-NC-ND

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

Otros archivos y enlaces

INTEGRALES SINGULARES, TEORIA GEOMETRICA DE LA MEDIDA Y EDP'S
Tolsa Domenech, X. (Principal Investigator), Dabrowski ., D. M. (Colaborador/a), Gallegos Saliner, J. M. (Colaborador/a), Guillen Mola, I. (Colaborador/a), Molero Casanova, A. (Colaborador/a), Prats Soler, M. (Colaborador/a), Sakellaris , G. (Colaborador/a), Martin Pedret, J. (Investigador/a), Prat Baiget, L. (Investigador/a), Hernandez Garcia, J. (Colaborador/a) & Ville Oikari, T. (Colaborador/a)
1/09/21 → 31/08/25
Proyecto: Proyectos y Ayudas de Investigación

Citar esto

@article{7deaa085bef148789af9964eb3b1e258,

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",

publisher = "Elsevier Masson SAS",

}

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 - http://www.scopus.com/inward/record.url?scp=85193551955&partnerID=8YFLogxK

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

Resumen

Acceder al documento

Otros archivos y enlaces

Huella

Proyectos

INTEGRALES SINGULARES, TEORIA GEOMETRICA DE LA MEDIDA Y EDP'S

Citar esto