Optimal convex domains for the first curl eigenvalue in dimension three

IF 17.7 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-04-24 DOI:10.1090/tran/8914

A. Enciso, Wadim Gerner, D. Peralta-Salas

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引用次数: 0

Abstract

We prove that there exists a bounded convex domain Ω ⊂ R 3 \Omega \subset \mathbb {R}^3 of fixed volume that minimizes the first positive curl eigenvalue among all other bounded convex domains of the same volume. We show that this optimal domain cannot be analytic, and that it cannot be stably convex if it is sufficiently smooth (e.g., of class C 1 , 1 C^{1,1} ). Existence results for uniformly Hölder optimal domains in a box (that is, contained in a fixed bounded domain D ⊂ R 3 D\subset \mathbb {R}^3 ) are also presented.

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三维第一个卷曲特征值的最佳凸域

我们证明存在一个固定体积的有界凸域 Ω ⊂ R 3 \Omega \subset \mathbb {R}^3，它在所有其他相同体积的有界凸域中最小化第一个正卷积特征值。我们证明了这个最优域不可能是解析的，而且如果它足够光滑（例如，类 C 1 , 1 C^{1,1} ），它就不可能是稳定凸的。我们还给出了盒中均匀霍尔德最优域（即包含在一个固定有界域 D ⊂ R 3 D\subset \mathbb {R}^3 中）的存在性结果。

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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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