去除小段后的频谱稳定性

Pub Date : 2024-02-29 DOI:10.1090/proc/16813

Xiang He

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引用次数: 0

摘要

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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Spectral stability under removal of small segments

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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