On Sobolev extension domains in Rⁿ

2009/04/06 by Pavel Shvartsman, Shvartsman, Pavel · 1 citation
Mathematics · #46E35 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0904.0909

openalex publication_date 2009/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a class of Sobolev W^k_p-extension domains Ω⊂ Rⁿ determined by a certain inner subhyperbolic metric in Ω. This enables us to characterize finitely connected Sobolev W¹_p-extension domains in R² for each p>2.

Citations

• Sobolev embeddings, extensions and measure density condition

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• A Note on Gradually Varied Functions and Harmonic Functions

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