Surface Concentration of Transmission Eigenfunctions

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Article number54
Journal / PublicationArchive for Rational Mechanics and Analysis
Volume247
Issue number3
Online published21 May 2023
Publication statusPublished - Jun 2023

Abstract

The transmission eigenvalue problem is a type of non-elliptic and non-selfadjoint spectral problem that arises in the wave scattering theory when invisibility/transparency occurs. The transmission eigenfunctions are the interior resonant modes inside the scattering medium. We are concerned with the geometric rigidity of the transmission eigenfunctions and show that they concentrate on the boundary surface of the underlying domain in two senses. This substantiates the recent numerical discovery in Chow et al. (SIAM J Imaging Sci, 14(3):946–975, 2021) on such an intriguing spectral phenomenon of the transmission resonance. Our argument is based a generalized Weyl’s law and certain novel ergodic properties of the coupled boundary layer-potential operators which are employed to analyze the generalized transmission eigenfunctions. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.

Citation Format(s)

Surface Concentration of Transmission Eigenfunctions. / CHOW, Yat Tin; DENG, Youjun; LIU, Hongyu et al.
In: Archive for Rational Mechanics and Analysis, Vol. 247, No. 3, 54, 06.2023.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review