Year: 2025
Type: article
Abstract: In this paper, we study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, we obtain the following results, Let $$1\leq q\leq p\leq \infty$$ 1 ≤ q ≤ p ≤ ∞ . Then a bounded $$(L^{1, p}, L^{1, q})$$ ( L 1 , p , L 1 , q ) -extension domain is also a $$(W^{1, p}, W^{1, q})$$ ( W 1 , p , W 1 , q ) -extension domain. Let $$1\leq q\leq p 1 ≤ q ≤ p < q ⋆ ≤ ∞ or $$n< q \leq p\leq \infty$$ n < q ≤ p ≤ ∞ . Then a bounded domain is a $$(W^{1, p}, W^{1, q})$$ ( W 1 , p , W 1 , q ) -extension domain if and only if it is an $$(L^{1, p}, L^{1, q})$$ ( L 1 , p , L 1 , q ) -extension domain. For
Source: Analysis Mathematica
Authors: P. Koskela, R. Mishra, Z. Zhu
Institutions: University of Jyväskylä, Beihang University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4415731580