Sobolev Versus Homogeneous Sobolev Extension

2024/11/18 by Pekka Koskela, Koskela, Pekka, Riddhi Mishra +3 · 1 citation
Engineering · Social Sciences · #30L99 #46E35 #FOS: Mathematics #Fatigue and fracture mechanics #Functional Analysis (math.FA) #Historical Geopolitical and Social Dynamics

paper · pdf · doi:10.48550/arxiv.2411.11470

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, we obtain the following results. 1- Let 1≤ q≤ p≤ ∞. Then a bounded (L^{1, p}, L^{1, q})-extension domain is also a (W^{1, p}, W^{1, q})-extension domain. 2- Let 1≤ q≤ p

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• Sobolev Versus Homogeneous Sobolev II

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