关于平行四边形第二正诺伊曼特征值的优化问题

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2025-07-18 DOI:10.1112/mtk.70033

Vladimir Lotoreichik, Jonathan Rohleder

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引用次数: 0

摘要

最近Bogosel， Henrot和Michetti推测，在所有固定周长的平面凸域中，诺伊曼拉普拉斯算子的第二个正特征值被一个边长等于另一个边长两倍的矩形最大化。在这篇笔记中，我们证明了这个猜想在平行四边形区域内是成立的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A note on optimization of the second positive Neumann eigenvalue for parallelograms

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A note on optimization of the second positive Neumann eigenvalue for parallelograms

It has recently been conjectured by Bogosel, Henrot, and Michetti that the second positive eigenvalue of the Neumann Laplacian is maximized, among all planar convex domains of fixed perimeter, by the rectangle with one edge length equal to twice the other. In this note, we prove that this conjecture is true within the class of parallelogram domains.

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.