关于Maxwell方程的一个内Calderón算子和一个相关的Steklov本征问题
On an interior Calderón operator and a related Steklov eigenproblem for Maxwell's equations
摘要：
本文讨论了一个与内部Calderón算子和适当的Dirichlet-to-Neumann型映射有关的Maxwell方程的Steklov型问题。相应的Neumann-to-Dirichlet映射是紧的，这为相关的能量空间提供了Steklov本征函数的傅立叶基。与Auchmuty开发的拉普拉斯算子的方法类似，我们提供了自然的谱表示为适当的迹空间，为卡尔德龙算子本身和相应的边值问题的解决方案受到电或磁边界条件的腔。
英文摘要：
We discuss a Steklov-type problem for Maxwell's equations which is related to an interior Calderón operator and an appropriate Dirichlet-to-Neumann type map. The corresponding Neumann-to-Dirichlet map turns out to be compact and this provides a Fourier basis of Steklov eigenfunctions for the associated energy spaces. With an approach similar to that developed by Auchmuty for the Laplace operator, we provide natural spectral representations for the appropriate trace spaces, for the Calderón operator itself and for the solutions of the corresponding boundary value problems subject to electric or magnetic boundary conditions on a cavity.
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