A Geometric Bound on the Lowest Magnetic Neumann Eigenvalue via the Torsion Function

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-08-08 DOI:10.1137/23m1624658

Ayman Kachmar, Vladimir Lotoreichik

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5723-5745, August 2024.
Abstract. We obtain an upper bound on the lowest magnetic Neumann eigenvalue of a bounded, convex, smooth, planar domain with moderate intensity of the homogeneous magnetic field. This bound is given as a product of a purely geometric factor expressed in terms of the torsion function and of the lowest magnetic Neumann eigenvalue of the disk having the same maximal value of the torsion function as the domain. The bound is sharp in the sense that equality is attained for disks. Furthermore, we derive from our upper bound that the lowest magnetic Neumann eigenvalue with the homogeneous magnetic field is maximized by the disk among all ellipses of fixed area provided that the intensity of the magnetic field does not exceed an explicit constant dependent only on the fixed area.

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通过扭转函数对最低磁性诺依曼特征值的几何约束

SIAM 数学分析期刊》，第 56 卷第 4 期，第 5723-5745 页，2024 年 8 月。摘要。我们得到了具有中等强度同相磁场的有界、凸、光滑平面域的最低磁性诺依曼特征值的上界。该界值是以扭转函数表示的纯几何因子与具有与该域相同最大扭转函数值的圆盘的最低磁性诺依曼特征值的乘积给出的。这个界限是尖锐的，因为对于磁盘来说，这个界限是相等的。此外，我们还从上界推导出，只要磁场强度不超过一个仅取决于固定区域的显式常数，在所有固定区域的椭圆中，磁盘的同相磁场的最低磁性诺依曼特征值是最大的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.