Sobolev extension in a simple case

IF 2.1 2区 数学 Q1 MATHEMATICS Advanced Nonlinear Studies Pub Date : 2024-05-24 DOI:10.1515/ans-2023-0132
Marjorie Drake, Charles Fefferman, Kevin Ren, Anna Skorobogatova
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引用次数: 0

Abstract

In this paper, we establish the existence of a bounded, linear extension operator T : L 2 , p ( E ) L 2 , p ( R 2 ) $T :{L}^{2,p}\left(E\right)\to {L}^{2,p}\left({\mathbb{R}}^{2}\right)$ when 1 < p < 2 and E is a finite subset of R 2 ${\mathbb{R}}^{2}$ contained in a line.
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简单情况下的索波列夫扩展
在本文中,当 1 < p < 2 且 E 是 R 2 的有限子集 ${\mathbb{R}}^{2}$ 包含在一条直线中时,我们建立了有界线性扩展算子 T : L 2 , p ( E ) → L 2 , p ( R 2 ) $T :{L}^{2,p}\left(E\right)/to {L}^{2,p}\left({\mathbb{R}}^{2}\right)$ 的存在性。
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来源期刊
CiteScore
3.00
自引率
5.60%
发文量
22
审稿时长
12 months
期刊介绍: Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.
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