Electromagnetic interior transmission eigenvalue problem for an inhomogeneous medium with a conductive boundary

Yuebin Hao

doi:10.3934/cpaa.2020068

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2020, Volume 19, Issue 3: 1387-1397. Doi: 10.3934/cpaa.2020068

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Electromagnetic interior transmission eigenvalue problem for an inhomogeneous medium with a conductive boundary

Yuebin Hao

School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China

Received: February 28, 2019

Revised: August 31, 2019

Published: February 2020

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Abstract

The interior transmission eigenvalue problem plays a basic role in the study of inverse scattering problems for an inhomogeneous medium. In this paper, we consider the electromagnetic interior transmission eigenvalue problem for an inhomogeneous medium with conductive boundary. Our main focus is to understand the associated eigenvalue problem, more specifically to prove the transmission eigenvalues form a discrete set and show that they exist by employing a variety of variational techniques under various assumptions on the index of refraction.

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Mathematics Subject Classification: Primary: 35Q61, 35P25; Secondary: 35J15.

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