Bi-Sobolev extensions
Complex Variables
2022-11-17 v1
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.
Cite
@article{arxiv.2211.08498,
title = {Bi-Sobolev extensions},
author = {Aleksis Koski and Jani Onninen},
journal= {arXiv preprint arXiv:2211.08498},
year = {2022}
}
Comments
18 pages, 2 figures