SIAM Journal on Applied Mathematics, Volume 80, Issue 2, Page 881-905, January 2020.
The Stekloff eigenvalue problem has been a recent problem of interest due to its potential use in the nondestructive testing of materials, but it suffers from two shortcomings that are common among this class of eigenvalue methods: it is not known in general if Stekloff eigenvalues exist in the case of complex coefficients, and there exists no mechanism by which to increase their sensitivity to changes in the material properties of the medium under consideration. We present a variation of the Stekloff eigenvalue problem which overcomes both of these issues by the introduction of a certain operator in the boundary condition, and we provide numerical examples to examine the practical consequences of this variation. We discuss this idea in the broader context of what might be called tailored eigenvalue methods, in which the eigenvalue problem is designed to ensure favorable theoretical or practical results.

中文翻译：

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反向散射中的痕量类Stekloff特征值问题分析

SIAM应用数学杂志，第80卷，第2期，第881-905页，2020年1月。
由于Stekloff特征值在材料的非破坏性测试中的潜在用途，因此一直是一个令人关注的新问题，但是它存在两个此类特征值方法共有的缺点：通常不知道Stekloff特征值是否存在于材料中。在复数系数的情况下，没有机制可以提高它们对所考虑介质的材料特性变化的敏感性。我们提出了Stekloff特征值问题的一种变体，通过在边界条件下引入某个算子来克服了这两个问题，并提供了数值示例来检验这种变体的实际后果。我们将在更广泛的范围内讨论量身定制的特征值方法，