多边形上拉普拉斯特征函数的临界点

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2021-08-23 DOI:10.1080/03605302.2022.2062572

C. Judge, Sugata Mondal

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引用次数: 3

摘要

摘要研究了多边形域上拉普拉斯特征函数的临界点，重点研究了第二诺伊曼特征函数。我们证明了如果每个凸四边形都不存在具有内临界点的第二个诺伊曼特征函数，则存在一个具有不稳定临界点的凸四边形。我们还证明了在没有正交边的Lip-1多边形上的第二个诺伊曼特征函数的每个临界点都是一个锐顶点。

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Critical points of Laplace eigenfunctions on polygons

Abstract We study the critical points of Laplace eigenfunctions on polygonal domains with a focus on the second Neumann eigenfunction. We show that if each convex quadrilaterals has no second Neumann eigenfunction with an interior critical point, then there exists a convex quadrilateral with an unstable critical point. We also show that each critical point of a second-Neumann eigenfunction on a Lip-1 polygon with no orthogonal sides is an acute vertex.

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来源期刊

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.