Schoenflies solutions of conformal boundary values may fail to be\n Sobolev

2018/08/30 by Yi Ru‐Ya Zhang, Zhang, Yi Ru-Ya · 1 citation
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1808.10392

openalex publication_date 2018/08/30 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

We show that there exists a planar Jordan domains \Ω with boundary of\nHausdorff dimension 1 such that, for any conformal maps \φ colon\n mathbb D \→ \Ω, any homeomorphic extension of \φ or\n\φ^-1 to the entire plane is not in W^{1, ,1} _{rm loc} (or even not\nin BV _{rm loc}).\n

Cited by

• Homeomorphic Sobolev extensions and integrability of hyperbolic metric

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