6533b86dfe1ef96bd12c96de

RESEARCH PRODUCT

Bi-Sobolev extensions

Aleksis KoskiJani Onninen

subject

Sobolev extensionskvasikonformikuvauksetMathematics - Complex VariablesPrimary 46E35 30C62. Secondary 58E20FOS: Mathematicsharmonic extensionquasiconformal mapping and mapping of finite distortionSobolev homeomorphismsComplex Variables (math.CV)Beurling-Ahlfors extension

description

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.

yearjournalcountryeditionlanguage
2022-11-15
http://arxiv.org/abs/2211.08498