Homeomorphic Sobolev extensions of parametrizations of Jordan curves

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Homeomorphic Sobolev extensions of parametrizations of Jordan curves
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)