论文标题
在导电传输本征函数附近消失
On vanishing near corners of conductive transmission eigenfunctions
论文作者
论文摘要
在本文中，我们考虑了与一般导电传输条件相关的传输特征值问题，并研究了传输本征函数的几何结构。我们证明，在一对透射本征的HERGLOTZ近似方面，在轻度的规律性条件下，本征函数必须消失在边界上的一个角落。 HERGLOTZ近似可以被视为平面波的透射量函数的傅立叶变换，并且可以使用转化函数的生长速率来表征基础波函数的规律性。本文中得出的几何结构包括[5,19]中的相关结果作为特殊情况，并验证拐角周围消失是传输本征函数的通用局部几何特性。
In this paper, we consider the transmission eigenvalue problem associated with a general conductive transmission condition and study the geometric structures of the transmission eigenfunctions. We prove that under a mild regularity condition in terms of the Herglotz approximations of one of the pair of the transmission eigenfunctions, the eigenfunctions must be vanishing around a corner on the boundary. The Herglotz approximation can be regarded as the Fourier transform of the transmission eigenfunction in terms of the plane waves, and the growth rate of the transformed function can be used to characterize the regularity of the underlying wave function. The geometric structures derived in this paper include the related results in [5,19] as special cases and verify that the vanishing around corners is a generic local geometric property of the transmission eigenfunctions.
