A variational characterization for the shift of eigenvalues caused by a general type of perturbation is derived for second order self-adjoint elliptic differential operators. This result allows the direct extension of asymptotic formulae from simple eigenvalues to repeated ones. Some examples of particular interest are presented theoretically and numerically for the Laplacian operator for the following domain perturbations: excision of a small hole, local change of conductivity, small boundary deformation.

中文翻译：

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扰动的自伴椭圆算子的重复特征值的渐近行为

对于二阶自伴椭圆微分算子，推导了由一般类型的摄动引起的特征值偏移的变化特征。该结果允许渐近公式从简单特征值直接扩展到重复的特征值。对于拉普拉斯算子，以下域摄动在理论上和数值上给出了一些特别有趣的示例：小孔的切除，电导率的局部变化，小边界变形。