Discreteness of interior transmission eigenvalues revisited
Discreteness of interior transmission eigenvalues revisited
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DOI：
10.1007/s00526-017-1143-7
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发表时间：
2016-10
影响因子：
2.1
通讯作者：
Hoai-Minh Nguyen;Quoc-Hung Nguyen
中科院分区：
文献类型：
--
作者：
Hoai-Minh Nguyen;Quoc-Hung Nguyen
本文主要研究传输本征值问题的离散性。众所周知，这个问题不是自伴的，先验估计是非标准的，一般不成立。使用了两种方法。第一种是基于乘子技术的，第二种是基于傅立叶分析的。分析的重点是建立柯西问题在不同条件下的紧性和唯一性。利用这些方法，我们能够重新发现文献中的许多已知离散性结果，并得到各种新的结果，这些结果只需要边界附近的信息，而边界上的系数可能没有对比性。
This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the multiplier technique and the second one is based on the Fourier analysis. The key point of the analysis is to establish the compactness and the uniqueness for Cauchy problems under various conditions. Using these approaches, we are able to rediscover quite a few known discreteness results in the literature and obtain various new results for which only the information near the boundary are required and there might be no contrast of the coefficients on the boundary.