论文标题
Bi-Sobolev扩展
Bi-Sobolev extensions
论文作者
论文摘要
我们给出了圆同构的全部特征，该圆形同构具有有限的BI-SOBOLOLEV NORM的单位磁盘的同态扩展。作为特殊情况，获得了著名的beurling-ahlfors扩展定理的双符符号变体。此外，我们表明现有的扩展技术，例如应用谐波或Beurling-ahlfors操作员在退化的环境中工作较差。这也为Karafyllia和Ntalampekos的问题提供了肯定的答案。
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.
