The existence of an infinite discrete set of transmission eigenvalues

Cakoni Fioralba; Gintides Drossos; Haddar Houssem

doi:10.1137/090769338

The existence of an infinite discrete set of transmission eigenvalues

Cakoni Fioralba, Gintides Drossos, Haddar Houssem

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the existence of an infinite discrete set of transmission eigenvalues corresponding to the scattering problem for isotropic and anisotropic inhomogeneous media for both the Helmholtz and Maxwell's equations. Our discussion includes the case of the interior transmission problem for an inhomogeneous medium with cavities, i.e., subregions with contrast zero.

Original language	English
Pages (from-to)	237-255
Number of pages	19
Journal	SIAM Journal on Mathematical Analysis
Volume	42
Issue number	1
DOIs	https://doi.org/10.1137/090769338
Publication status	Published - 1 Jan 2010

Keywords

Inhomogeneous medium
Interior transmission problem
Inverse scattering
Transmission eigenvalues

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10.1137/090769338

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title = "The existence of an infinite discrete set of transmission eigenvalues",

abstract = "We prove the existence of an infinite discrete set of transmission eigenvalues corresponding to the scattering problem for isotropic and anisotropic inhomogeneous media for both the Helmholtz and Maxwell's equations. Our discussion includes the case of the interior transmission problem for an inhomogeneous medium with cavities, i.e., subregions with contrast zero.",

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author = "Cakoni Fioralba and Gintides Drossos and Haddar Houssem",

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AU - Houssem, Haddar

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N2 - We prove the existence of an infinite discrete set of transmission eigenvalues corresponding to the scattering problem for isotropic and anisotropic inhomogeneous media for both the Helmholtz and Maxwell's equations. Our discussion includes the case of the interior transmission problem for an inhomogeneous medium with cavities, i.e., subregions with contrast zero.

AB - We prove the existence of an infinite discrete set of transmission eigenvalues corresponding to the scattering problem for isotropic and anisotropic inhomogeneous media for both the Helmholtz and Maxwell's equations. Our discussion includes the case of the interior transmission problem for an inhomogeneous medium with cavities, i.e., subregions with contrast zero.

KW - Inhomogeneous medium

KW - Interior transmission problem

KW - Inverse scattering

KW - Transmission eigenvalues

U2 - 10.1137/090769338

DO - 10.1137/090769338

M3 - Article

AN - SCOPUS:77950574432

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SP - 237

EP - 255

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

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ER -

The existence of an infinite discrete set of transmission eigenvalues

Abstract

Keywords

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