论文标题
关于修改的Maxwell Steklov特征值的存在和稳定性
On the existence and stability of modified Maxwell Steklov eigenvalues
论文作者
论文摘要
近几十年来，具有特征值作为目标特征的定性反向散射方法受到了很多关注。要了解这些方法，有关相关特征值问题的特性的知识至关重要。但是，即使存在于这种（非偶然之间）问题的特征值也是一个挑战性的问题，并且在不切实际的假设或特征值问题的平滑下，吸收媒体的现有结果通常也是建立的。我们提出了一种技术，以证明在现实假设下，无限地存在许多特征值。特别是我们考虑标量和修改的麦克斯韦（Maxwell）nonselfadjoint steklov特征值问题。此外，我们在材料参数变化方面给出了特征值的稳定性结果。与现有结果区别，本文的分析仅需要最少的规律性假设。这样我们意味着，域的规律性不需要比Lipschitz更好，并且仅认为材料系数是零件的$ w^{1，\ infty} $。同样，特征值的稳定性估计仅以$ l^p $ -norms（$ p <\ infty $）的材料扰动获得。
In recent decades qualitative inverse scattering methods with eigenvalues as target signatures received much attention. To understand those methods a knowledge on the properties of the related eigenvalue problems is essential. However, even the existence of eigenvalues for such (nonselfadjoint) problems is a challenging question and existing results for absorbing media are usually established under unrealistic assumptions or a smoothing of the eigenvalue problem. We present a technique to prove the existence of infinitely many eigenvalues for such problems under realistic assumptions. In particular we consider the class of scalar and modified Maxwell nonselfadjoint Steklov eigenvalue problems. In addition, we present stability results for the eigenvalues with respect to changes in the material parameters. In distinction to existing results the analysis of the present article requires only minimal regularity assumptions. By that we mean that the regularity of the domain is not required to be better than Lipschitz, and the material coefficients are only assumed to be piece-wise $W^{1,\infty}$. Also the stability estimates for eigenvalues are obtained solely in $L^p$-norms ($p<\infty$) of the material perturbations.
