Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 791-796

SCHOENFLIES SOLUTIONS OF CONFORMAL BOUNDARY VALUES MAY FAIL TO BE SOBOLEV

Yi Ru-Ya Zhang

Hausdorff Center for Mathematics
Endenicher Allee 60, D-53115 Bonn, Germany; yizhang 'at' math.uni-bonn.de

Abstract. There exists a planar Jordan domains Ω with 1-Hausdorff dimensional boundary such that, for any conformal map φ : D → Ω, any homeomorphic extensions to the entire plane of either φ or φ^-1 cannot be in W^1,1_loc class (or even not in BV_loc).

2010 Mathematics Subject Classification: Primary 30C70.

Key words: Sobolev homeomorphism, Jordan–Schoenflies theorem.

Reference to this article: Y. R.-Y. Zhang: Schoenflies solutions of conformal boundary values may fail to be Sobolev. Ann. Acad. Sci. Fenn. Math. 44 (2019), 791-796.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4441