论文标题
电磁stekloff特征值的存在和稳定性具有微量类修改
Existence and stability of electromagnetic Stekloff eigenvalues with a trace class modification
论文作者
论文摘要
最新感兴趣的领域是对散射理论中特征值问题的发展和研究，该理论可能提供潜在的目标特征，以用于材料的非破坏性测试。我们考虑了取决于平滑参数的电磁stekloff特征值问题的概括，为此，我们建立了两个以前对于这种类型的特征值问题而无法获得的主要结果。首先，我们使用痕量类操作员的理论证明，即使是吸收培养基，也有足够高的平滑度存在无限的特征值。其次，我们利用Maxwell方程的规律性结果，以建立相对于材料系数的特征值的稳定性结果，并且我们表明，随着平滑参数将其接收到零。
A recent area of interest is the development and study of eigenvalue problems arising in scattering theory that may provide potential target signatures for use in nondestructive testing of materials. We consider a generalization of the electromagnetic Stekloff eigenvalue problem that depends upon a smoothing parameter, for which we establish two main results that were previously unavailable for this type of eigenvalue problem. First, we use the theory of trace class operators to prove that infinitely many eigenvalues exist for a sufficiently high degree of smoothing, even for an absorbing medium. Second, we leverage regularity results for Maxwell's equations in order to establish stability results for the eigenvalues with respect to the material coefficients, and we show that this generalized class of Stekloff eigenvalues converges to the standard class as the smoothing parameter approaches zero.
