Homeomorphic Sobolev extensions of parametrizations of Jordan curves

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F25%3A00380567" target="_blank" >RIV/68407700:21240/25:00380567 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jfa.2024.110721" target="_blank" >https://doi.org/10.1016/j.jfa.2024.110721</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jfa.2024.110721" target="_blank" >10.1016/j.jfa.2024.110721</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Homeomorphic Sobolev extensions of parametrizations of Jordan curves

Popis výsledku v původním jazyce

Each homeomorphic parametrization of a Jordan curve via the unit circle extends to a homeomorphism of the entire plane. It is a natural question to ask if such a homeomorphism can be chosen so as to have some Sobolev regularity. This prompts the simplified question: for a homeomorphic embedding of the unit circle into the plane, when can we find a homeomorphism from the unit disk that has the same boundary values and integrable first-order distributional derivatives? We give the optimal geometric criterion for the interior Jordan domain so that there exists a Sobolev homeomorphic extension for any homeomorphic parametrization of the Jordan curve. The problem is partially motivated by trying to understand which boundary values can correspond to deformations of finite energy.

Název v anglickém jazyce

Homeomorphic Sobolev extensions of parametrizations of Jordan curves

Popis výsledku anglicky

Each homeomorphic parametrization of a Jordan curve via the unit circle extends to a homeomorphism of the entire plane. It is a natural question to ask if such a homeomorphism can be chosen so as to have some Sobolev regularity. This prompts the simplified question: for a homeomorphic embedding of the unit circle into the plane, when can we find a homeomorphism from the unit disk that has the same boundary values and integrable first-order distributional derivatives? We give the optimal geometric criterion for the interior Jordan domain so that there exists a Sobolev homeomorphic extension for any homeomorphic parametrization of the Jordan curve. The problem is partially motivated by trying to understand which boundary values can correspond to deformations of finite energy.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

JOURNAL OF FUNCTIONAL ANALYSIS

ISSN

0022-1236

e-ISSN

1096-0783

Svazek periodika

288

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

—

Kód UT WoS článku

001374707700001

EID výsledku v databázi Scopus

2-s2.0-85207897617