论文标题
关于麦克斯韦方程的传输特征值的离散性
On the Discreteness of Transmission Eigenvalues for the Maxwell Equations
论文作者
论文摘要
在本文中，我们建立了麦克斯韦方程的传输特征值的离散性。更准确地说，我们表明，如果电磁参数$ \ eps，\，\，μ，\，\，\，\，\，\，\，\，\，\，\ hmu $在不良性和背景表征的方程式中，则在边界的某些情况下，; \ heps $，$μ\ neq \ hmu $和$ \ eps/μ\ neq \ heps/ \ hmu $在边界上。这些是易于检查的系数上的一般假设。据我们所知，我们的论文是第一个建立麦克斯韦方程的传输特征值的离散性，而不假设对形成$ \ eps- \ heps $和$μ-\ hmu $的符号组合有任何限制，并允许所有电源范围内的电源范围内的任何一个均无含量的电源，并且允许均一以外的范围。在文献中经常假设的不变。
In this paper, we establish the discreteness of transmission eigenvalues for Maxwell's equations. More precisely, we show that the spectrum of the transmission eigenvalue problem is discrete, if the electromagnetic parameters $\eps, \, μ, \, \heps, \, \hmu$ in the equations characterizing the inhomogeneity and background, are smooth in some neighborhood of the boundary, isotropic on the boundary, and satisfy the conditions $\eps \neq \heps$, $μ\neq \hmu$, and $\eps/ μ\neq \heps/ \hmu$ on the boundary. These are quite general assumptions on the coefficients which are easy to check. To our knowledge, our paper is the first to establish discreteness of transmission eigenvalues for Maxwell's equations without assuming any restrictions on the sign combination of the contrasts $\eps-\heps$ and $μ- \hmu$ near the boundary, and allowing for all the electromagnetic parameters to be inhomogeneous and anisotropic, except for on the boundary where they are isotropic but not necessarily constant as it is often assumed in the literature.
