Optimal convex domains for the first curl eigenvalue in dimension three

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society 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

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.