论文标题
在室内calderón操作员和麦克斯韦方程的相关steklov特征问题上
On an interior Calderón operator and a related Steklov eigenproblem for Maxwell's equations
论文作者
论文摘要
我们讨论了Maxwell方程的Steklov型问题，该问题与内部Calderón操作员以及适当的Dirichlet到Neumann类型地图有关。相应的neumann到dirichlet映射原来是紧凑的，这为相关能量空间提供了Steklov特征函数的傅立叶基础。通过类似于Auchmuty为Laplace操作员开发的方法，我们为适当的痕量空间，Calderón运算符本身以及相应的边界值问题的解决方案提供了自然的光谱表示，遵守腔内的电或磁性边界条件。
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.
