On the Whitney problem for weighted Sobolev spaces
- Authors: Tyulenev A.I.1,2, Vodop’yanov S.K.1,2
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Affiliations:
- Steklov Mathematical Institute
- Sobolev Institute of Mathematics, Siberian Branch
- Issue: Vol 95, No 1 (2017)
- Pages: 79-83
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224822
- DOI: https://doi.org/10.1134/S1064562417010276
- ID: 224822
Cite item
Abstract
Given a closed weakly regular d-thick subset S of ℝn, we prove the existence of a bounded linear extension operator Ext: Tr|SWp1 (ℝn, γ) → Wp1(ℝn, γ) for p ∈ (1, ∞), 0 ≤ d ≤ n, r ∈ (max{1, n − d}, p), l ∈ ℕ, and \(\gamma \in {A_{\frac{p}{r}}}\)(ℝn). In particular, we prove that a linear bounded trace space exists in the case where S is the closure of an arbitrary domain in ℝn, γ ≡ 1, and p > n − 1. The obtained results supplement those of previous studies, in which a similar problem was considered either in the case of p ∈ (n, ∞) without constraints on the set S or in the case of p ∈ (1, ∞) under stronger constraints on the set S.
About the authors
A. I. Tyulenev
Steklov Mathematical Institute; Sobolev Institute of Mathematics, Siberian Branch
Author for correspondence.
Email: tyulenev-math@yandex.ru
Russian Federation, ul. Gubkina 8, Moscow, 119991; pr. Akademika Koptyuga 4, Novosibirsk, 630090
S. K. Vodop’yanov
Steklov Mathematical Institute; Sobolev Institute of Mathematics, Siberian Branch
Email: tyulenev-math@yandex.ru
Russian Federation, ul. Gubkina 8, Moscow, 119991; pr. Akademika Koptyuga 4, Novosibirsk, 630090