Bi-Sobolev Extensions

Aleksis Koski*, Jani Onninen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Article number301
Number of pages18
JournalJOURNAL OF GEOMETRIC ANALYSIS
Volume33
Issue number9
DOIs
Publication statusPublished - Sept 2023
MoE publication typeA1 Journal article-refereed

Keywords

  • Beurling–Ahlfors extension
  • Harmonic extension
  • Quasiconformal mapping and mapping of finite distortion
  • Sobolev extensions
  • Sobolev homeomorphisms

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