In this paper we consider a class of singularly perturbed domains, obtained by attaching a cylindrical tube to a fixed bounded region and letting its section shrink to zero. We use an Almgren-type monotonicity formula to evaluate the sharp convergence rate of perturbed simple eigenvalues, via Courant-Fischer Min-Max characterization and blow-up analysis for scaled eigenfunctions.

中文翻译：

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具有收缩管的域中特征值的急剧收敛速度

在本文中，我们考虑一类奇异扰动域，通过将圆柱管连接到固定有界区域并使其截面收缩为零而获得。我们使用 Almgren 型单调性公式通过 Courant-Fischer Min-Max 表征和缩放特征函数的放大分析来评估扰动的简单特征值的急剧收敛速度。