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Sobolev Embedding Theorems for Spaces Wk, p(x)(Ω)

✍ Scribed by Xianling Fan; Jishen Shen; Dun Zhao

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 103 KB
Volume: 262
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7618

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✦ Synopsis

This paper gives a Sobolev-type embedding theorem for the generalized Lebesgue-Sobolev space

, where is an open domain in R N N ≥ 2 with cone property, and p x is a Lipschitz continuous function defined on satisfying 1 < p -≤ p + < N k . The main result can be stated as follows: for any measurable function q x x ∈ with p x ≤ q x ≤ p * x = Np x N -kp x there exists a continuous embedding from W k p x to L q x .

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Sobolev Embedding Theorems for Spaces Wk,&#xa0;p(x)(Ω)

✦ Synopsis

Sobolev Embedding Theorems for Spaces Wk, p(x)(Ω)