The interior transmission problem for regions with cavities

Fioralba Cakoni; David Colton; Houssem Haddar

doi:10.1137/090754637

The interior transmission problem for regions with cavities

Fioralba Cakoni, David Colton, Houssem Haddar

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

53 Scopus citations

Abstract

We consider the interior transmission problem in the case when the inhomogeneous medium has cavities, i.e., regions in which the index of refraction is the same as the host medium. In this case we establish the Fredholm property for this problem and show that transmission eigenvalues exist and form a discrete set. We also derive Faber-Krahn-type inequalities for the transmission eigenvalues.

Original language	English (US)
Pages (from-to)	145-162
Number of pages	18
Journal	SIAM Journal on Mathematical Analysis
Volume	42
Issue number	1
DOIs	https://doi.org/10.1137/090754637
State	Published - 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

Keywords

Inhomogeneous medium
Interior transmission problem
Inverse scattering
Trans-mission eigenvalues

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10.1137/090754637

Cite this

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title = "The interior transmission problem for regions with cavities",

abstract = "We consider the interior transmission problem in the case when the inhomogeneous medium has cavities, i.e., regions in which the index of refraction is the same as the host medium. In this case we establish the Fredholm property for this problem and show that transmission eigenvalues exist and form a discrete set. We also derive Faber-Krahn-type inequalities for the transmission eigenvalues.",

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author = "Fioralba Cakoni and David Colton and Houssem Haddar",

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T1 - The interior transmission problem for regions with cavities

AU - Cakoni, Fioralba

AU - Colton, David

AU - Haddar, Houssem

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Y1 - 2010

N2 - We consider the interior transmission problem in the case when the inhomogeneous medium has cavities, i.e., regions in which the index of refraction is the same as the host medium. In this case we establish the Fredholm property for this problem and show that transmission eigenvalues exist and form a discrete set. We also derive Faber-Krahn-type inequalities for the transmission eigenvalues.

AB - We consider the interior transmission problem in the case when the inhomogeneous medium has cavities, i.e., regions in which the index of refraction is the same as the host medium. In this case we establish the Fredholm property for this problem and show that transmission eigenvalues exist and form a discrete set. We also derive Faber-Krahn-type inequalities for the transmission eigenvalues.

KW - Inhomogeneous medium

KW - Interior transmission problem

KW - Inverse scattering

KW - Trans-mission eigenvalues

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DO - 10.1137/090754637

M3 - Article

AN - SCOPUS:77954406522

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EP - 162

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

The interior transmission problem for regions with cavities

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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