Semiclassical parametrix for the Maxwell equation and applications to the electromagnetic transmission eigenvalues

We introduce an analog of the Dirichlet-to-Neumann map for the Maxwell equation in a bounded domain. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol. As an application, we obtain a parabolic region f...

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Bibliographic Details
Published in:Research in the mathematical sciences 2021-09, Vol.8 (3), Article 35
Main Author: Vodev, Georgi
Format: Article
Language:English
Subjects:
Analysis of PDEs
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Dirichlet problem
Eigenvalues
Electromagnetic wave transmission
Mathematical Physics
Mathematics
Mathematics and Statistics
Maxwell's equations
Transmission Eigen Values and Related Spectral Problems in Scattering Theory
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Summary:We introduce an analog of the Dirichlet-to-Neumann map for the Maxwell equation in a bounded domain. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol. As an application, we obtain a parabolic region free of the transmission eigenvalues associated with the Maxwell equation.
ISSN:2522-0144
2197-9847
DOI:10.1007/s40687-021-00272-5