Geometric Structures of Maxwell’s Transmission Eigenfunctions and Applications

Huaian Diao and Hongyu Liu
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Huaian Diao: Jilin University, School of Mathematics
Hongyu Liu: City University of Hong Kong, Department of Mathematics

Chapter Chapter 9 in Spectral Geometry and Inverse Scattering Theory, 2023, pp 243-257 from Springer

Abstract: Abstract In this chapter, we are mainly concerned with the time-harmonic Maxwell system, where we follow the treatment in Blåsten et al. (Anal. PDE, 14(7), 2207–2224 (2021)). Let ω ∈ ℝ + $$\omega \in \mathbb {R}_+$$ denote the frequency, and let ε 0 , μ 0 ∈ ℝ + $$\varepsilon _0, \mu _0\in \mathbb {R}_+$$ , respectively, signify the electric permittivity and magnetic permeability of a uniformly homogeneous space. Throughout, we let E and H denote, respectively, the electric and magnetic fields, which are ℂ 3 $$\mathbb {C}^3$$ -valued functions. We first introduce the notion of the corner and the corresponding Maxwell system locally around the corner.

Date: 2023
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DOI: 10.1007/978-3-031-34615-6_9

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