The extension property for domains with one singular point

2021/10/14 by Pekka Koskela, Zheng Zhu, Koskela, Pekka +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2110.07565

openalex publication_date 2021/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An arbitrary outward cuspidal domain is shown to be bi-Lipschitz equivalent to a Lipschitz outward cuspidal domain via a global transformation. This allows us to extend earlier Sobolev extension results on Lipschitz outward cuspidal domains from the work of Maz'ya and Poborchi to arbitrary outward cuspidal domains. We also establish a limit case of extension results on outward cuspidal domains.

Citations

• Sobolev embeddings, extensions and measure density condition

Cited by

• Sobolev Versus Homogeneous Sobolev II

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