对于某些双相积分没有Lavrentiev隙

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-08-30 DOI:10.1515/acv-2021-0109

Filomena De Filippis, F. Leonetti

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引用次数: 5

摘要

摘要证明了非自治函子＿＿ (u)是∫Ω f ＿ (x)，D ＿ (u) ＿ (x)) ＿𝑑x, \mathcal{F} (u) \coloneqq\int ＿ {\Omega} f(x,Du(x))\，dx，其中f ＿ (x, z) {f(x,z)}对于x∈Ω是α-Hölder连续的，∧∈Ω {x\in\Omega\subset\mathbb{R} ^ {n}}满足(p，q) {(p,q)} -生长条件| z | p≤f(x,z)≤L(1+ | z | q)， \lvert z \rvert ^ {p}\leqslant f(x,z) \leqslant L(1+ \lvert z \rvert ^ {q})，其中1 < p < q < p≠(n + α n) {1本文章由计算机程序翻译，如有差异，请以英文原文为准。

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No Lavrentiev gap for some double phase integrals

Abstract We prove the absence of the Lavrentiev gap for non-autonomous functionals ℱ ⁢ ( u ) ≔ ∫ Ω f ⁢ ( x , D ⁢ u ⁢ ( x ) ) ⁢ 𝑑 x , \mathcal{F}(u)\coloneqq\int_{\Omega}f(x,Du(x))\,dx, where the density f ⁢ ( x , z ) {f(x,z)} is α-Hölder continuous with respect to x ∈ Ω ⊂ ℝ n {x\in\Omega\subset\mathbb{R}^{n}} , it satisfies the ( p , q ) {(p,q)} -growth conditions | z | p ⩽ f ⁢ ( x , z ) ⩽ L ⁢ ( 1 + | z | q ) , \lvert z\rvert^{p}\leqslant f(x,z)\leqslant L(1+\lvert z\rvert^{q}), where 1 < p < q < p ⁢ ( n + α n ) {1

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.