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arXiv · 2211.08498

Bi-Sobolev extensions

Aleksis Koski·Jani Onninen
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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.

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Aleksis Koski, Jani Onninen. 2022-11-15. Bi-Sobolev extensions. https://arxiv.org/abs/2211.08498

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