Transmission eigenvalues

Fioralba Cakoni; Houssem Haddar

doi:10.1088/0266-5611/29/10/100201

Transmission eigenvalues

Fioralba Cakoni
, Houssem Haddar

University of Delaware

Research output: Contribution to journal › Review article › peer-review

Abstract

The 2013 special issue of Inverse Problems describes papers that are concerned with the question of existence of transmission eigenvalues and the structure of the associated transmission eigenfunctions. The three papers by respectively Robbiano, Blasten and Päivärinta and Lakshtanov and Vainberg provide newcomplementary results on the existence of transmission eigenvalues for the scalar problem under weak assumptions on the refractive index that mainly stipulates that the contrast does not change sign on the boundary. On the other hand, the paper by Bonnet-Ben Dhia and Chesnel addresses the Fredholm properties of the interior transmission problem when the contrast changes sign on the boundary, exhibiting cases where this property fails. Using more standard approaches, the existence and structure of transmission eigenvalues are analyzed in the paper by Delbary.

Original language	English
Article number	100201
Journal	Inverse Problems
Volume	29
Issue number	10
DOIs	https://doi.org/10.1088/0266-5611/29/10/100201
Publication status	Published - 1 Oct 2013

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title = "Transmission eigenvalues",

abstract = "The 2013 special issue of Inverse Problems describes papers that are concerned with the question of existence of transmission eigenvalues and the structure of the associated transmission eigenfunctions. The three papers by respectively Robbiano, Blasten and P{\"a}iv{\"a}rinta and Lakshtanov and Vainberg provide newcomplementary results on the existence of transmission eigenvalues for the scalar problem under weak assumptions on the refractive index that mainly stipulates that the contrast does not change sign on the boundary. On the other hand, the paper by Bonnet-Ben Dhia and Chesnel addresses the Fredholm properties of the interior transmission problem when the contrast changes sign on the boundary, exhibiting cases where this property fails. Using more standard approaches, the existence and structure of transmission eigenvalues are analyzed in the paper by Delbary.",

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AU - Haddar, Houssem

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N2 - The 2013 special issue of Inverse Problems describes papers that are concerned with the question of existence of transmission eigenvalues and the structure of the associated transmission eigenfunctions. The three papers by respectively Robbiano, Blasten and Päivärinta and Lakshtanov and Vainberg provide newcomplementary results on the existence of transmission eigenvalues for the scalar problem under weak assumptions on the refractive index that mainly stipulates that the contrast does not change sign on the boundary. On the other hand, the paper by Bonnet-Ben Dhia and Chesnel addresses the Fredholm properties of the interior transmission problem when the contrast changes sign on the boundary, exhibiting cases where this property fails. Using more standard approaches, the existence and structure of transmission eigenvalues are analyzed in the paper by Delbary.

AB - The 2013 special issue of Inverse Problems describes papers that are concerned with the question of existence of transmission eigenvalues and the structure of the associated transmission eigenfunctions. The three papers by respectively Robbiano, Blasten and Päivärinta and Lakshtanov and Vainberg provide newcomplementary results on the existence of transmission eigenvalues for the scalar problem under weak assumptions on the refractive index that mainly stipulates that the contrast does not change sign on the boundary. On the other hand, the paper by Bonnet-Ben Dhia and Chesnel addresses the Fredholm properties of the interior transmission problem when the contrast changes sign on the boundary, exhibiting cases where this property fails. Using more standard approaches, the existence and structure of transmission eigenvalues are analyzed in the paper by Delbary.

U2 - 10.1088/0266-5611/29/10/100201

DO - 10.1088/0266-5611/29/10/100201

M3 - Review article

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SN - 0266-5611

VL - 29

JO - Inverse Problems

JF - Inverse Problems

IS - 10

M1 - 100201

ER -

Transmission eigenvalues

Abstract

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