Spectral stability under removal of small segments

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-02-29 DOI:10.1090/proc/16813

Xiang He

引用次数: 0

Abstract

In the present paper, we deepen the works of L. Abatangelo, V. Felli, L. Hillairet and C. Léna on the asymptotic estimates of the eigenvalue variation under removal of segments from the domain in R 2 \mathbb {R}^2 . We get a sharp asymptotic estimate when the eigenvalue is simple and the removed segment is tangent to a nodal line of the associated eigenfunction. Moreover, we extend their results to the case when the eigenvalue is not simple.

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去除小段后的频谱稳定性

在本文中，我们深化了 L. Abatangelo、V. Felli、L. Hillairet 和 C. Léna 关于从 R 2 \mathbb {R}^2 中的域中移除线段时特征值变化的渐近估计的研究。当特征值简单且移除的线段与相关特征函数的节点线相切时，我们得到了一个尖锐的渐近估计值。此外，我们还将他们的结果扩展到了特征值不简单的情况。

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

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 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 shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, 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. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.