We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of the elementary symmetric functions of the eigenvalues splitting a multiple eigenvalue, as well as a Rellich-Nagy-type result describing the corresponding bifurcation phenomenon. We also address an isoperimetric problem and characterize the critical cavities for the symmetric functions of the eigenvalues subject to isovolumetric or isoperimetric domain perturbations and prove that balls are critical. We include known formulas for the eigenpairs in a ball and calculate the first one.

中文翻译：

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电磁腔的形状敏感性分析

我们研究了腔中时谐麦克斯韦方程的特征值对其形状变化的依赖性。分析涉及所有单特征值和多特征值。我们提供了分裂多个特征值的特征值的基本对称函数的相关性的解析结果，以及描述相应分叉现象的 Rellich-Nagy 型结果。我们还解决了等周问题，并描述了受等容或等周域扰动的特征值对称函数的临界腔，并证明球是关键的。我们包括球中特征对的已知公式并计算第一个。