论文标题
电磁腔的介电常数变化的一些结果
A few results on permittivity variations in electromagnetic cavities
论文作者
论文摘要
我们研究了介质的电介电常数$ \ varepsilon $的变化，研究了腔体中时谐波麦克斯韦方程的特征值。我们证明，与$ \ varepsilon $相对于$ \ varepsilon $，所有简单和多个特征值都是局部的。接下来，我们表明简单的特征值和多个特征值的对称函数在分析上取决于$ \ varepsilon $，我们为其在$ \ varepsilon $中的衍生产品提供了明确的公式。作为这些结果的应用，我们表明，对于一般介电常数，所有麦克斯韦特征值都很简单。
We study the eigenvalues of time-harmonic Maxwell's equations in a cavity upon changes in the electric permittivity $\varepsilon$ of the medium. We prove that all the eigenvalues, both simple and multiple, are locally Lipschitz continuous with respect to $\varepsilon$. Next, we show that simple eigenvalues and the symmetric functions of multiple eigenvalues depend real analytically upon $\varepsilon$ and we provide an explicit formula for their derivative in $\varepsilon$. As an application of these results, we show that for a generic permittivity all the Maxwell eigenvalues are simple.
