变指数Sobolev空间中的一致凸性

IF 2.2 3区综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Symmetry-Basel Pub Date : 2023-10-27 DOI:10.3390/sym15111988

Mostafa Bachar, Mohamed A. Khamsi, Osvaldo Méndez

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引用次数: 0

摘要

我们证明了在一个域Ω∧Rn中Sobolev空间W1,p(Ω)上混合范数Lp(l2)的模凸性，其唯一假设是指数p(x)离1有界，即我们包含supx∈Ωp(x)=∞的情况。特别地，当1<infx∈Ωp(x)≤supx∈Ωp(x)<∞且W01,p(Ω)为一致凸时，混合Sobolev范数为一致凸。

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Uniform Convexity in Variable Exponent Sobolev Spaces

We prove the modular convexity of the mixed norm Lp(ℓ2) on the Sobolev space W1,p(Ω) in a domain Ω⊂Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx∈Ωp(x)=∞. In particular, the mixed Sobolev norm is uniformly convex if 1

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来源期刊

Symmetry-Basel MULTIDISCIPLINARY SCIENCES-

CiteScore

5.40

自引率

11.10%

发文量

2276

审稿时长

14.88 days

期刊介绍： Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.