Sobolev Versus Homogeneous Sobolev II

2025/07/09 by Pekka Koskela, Koskela, Pekka, Riddhi Mishra +3
Mathematics · #30L99 #46E35 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2507.07072

openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, for a certain range of exponents p and q, we construct a (W^{1, p}, W^{1, q})-extension domain which is not an (L^{1, p}, L^{1, q})-extension domain.

Citations

• Sobolev Versus Homogeneous Sobolev Extension
• The extension property for domains with one singular point
• Pointwise inequalities for Sobolev functions on generalized cuspidal domains
• The volume of the boundary of a Sobolev (p,q)-extension domain

Related

• Sobolev Versus Homogeneous Sobolev Extension
• On Sobolev extension domains in Rⁿ
• Product of extension domains is still an extension domain
• Extension criteria for homogeneous Sobolev space of functions of one\n variable
• Extension in generalized Orlicz--Sobolev spaces