HIGH-FREQUENCY APPROXIMATION OF THE INTERIOR DIRICHLET-TO-NEUMANN MAP AND APPLICATIONS TO THE TRANSMISSION EIGENVALUES

被引：19

作者：

Vodev, Georgi ^{[1
]}

机构：

[1] Univ Nantes, Lab Math Jean Leray, Nantes, France

来源：

ANALYSIS & PDE | 2018年 / 11卷 / 01期

关键词：

Dirichlet-to-Neumann map; transmission eigenvalues; ASYMPTOTICS; NUMBER;

D O I：

10.2140/apde.2018.11.213

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the high-frequency behaviour of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a nonempty smooth boundary. We show that far from the real axis it can be approximated by a simpler operator. We use this fact to get new results concerning the location of the transmission eigenvalues on the complex plane. In some cases we obtain optimal transmission eigenvalue-free regions.

引用

页码：213 / 236

页数：24