2022/11/15 by Aleksis Koski, Koski, Aleksis, Jani Onninen +1 · 1 citation
Mathematics · Engineering · #Analytic and geometric function theory #Elasticity and Wave Propagation
paper · pdf · doi:10.48550/arxiv.2211.08498
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.