通过严格Faber-Krahn型不等式的第一特征值的定义域变分

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2022-02-08 DOI:10.57262/ade028-0708-537

T. Anoop, K. Kumar

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引用次数: 5

摘要

对于$d\geq2$和$\frac｛2d+2｝｛d+2｝＜p<\infty$，我们证明了极化条件下有界Lipschitz域$\Omega\subet\mathbb｛R｝^d$上$p$-Laplace算子的第一特征值$\lambda_1（\Omega）$的严格Faber-Krahn型不等式。我们将这个不等式应用于形式为$\Omega\setminus\mathscr｛O｝$的域上的障碍问题，其中$\mathscr{O｝\subet\subet\Omega$是一个障碍。在$\Omega$和$\mathscr｛O｝$上的一些几何假设下，我们证明了$\lambda_1（\Omega\setminus\mathscr{O｝）$关于$\mathscr{O｝$在$\Omega$中的某些平移和旋转的严格单调性。

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Domain variations of the first eigenvalue via a strict Faber-Krahn type inequality

For $d\geq 2$ and $\frac{2d+2}{d+2}

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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.

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