ON NEW SURFACE-LOCALIZED TRANSMISSION EIGENMODES

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

10 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)595-611
Journal / PublicationInverse Problems and Imaging
Volume16
Issue number3
Online publishedOct 2021
Publication statusPublished - Jun 2022

Abstract

Consider the transmission eigenvalue problem (Δ + k2n2)w = 0, (Δ + k2)v = 0 in Ω; w = v, ∂vw = ∂vv on ∂Ω. 
It is shown in [16] that there exists a sequence of eigenfunctions (wm, vm)m associated with k→ ∞ such that either {wm}m or {vm}m are surface-localized, depending on n > 1 or 0 < n < 1. In this paper, we discover a new type of surface-localized transmission eigenmodes by constructing a sequence of transmission eigenfunctions (wm, vm)mℕ associated with km → ∞ such that both {wm}mℕ and {vm}mℕ are surface-localized, no matter n > 1 or 0 < n < 1. Though our study is confined within the radial geometry, the construction is subtle and technical.

Research Area(s)

  • Transmission eigenfunctions, spectral geometry, surface localization, wave concentration, CORNERS, SCATTERING, BESSEL, EIGENFUNCTIONS, UNIQUENESS, BOUNDS, ZEROS

Citation Format(s)

ON NEW SURFACE-LOCALIZED TRANSMISSION EIGENMODES. / Deng, Youjun; Jiang, Yan; Liu, Hongyu et al.
In: Inverse Problems and Imaging, Vol. 16, No. 3, 06.2022, p. 595-611.

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