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

Department of Mathematical Sciences
University of Delaware

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

55 Citations (Scopus)

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
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
Publication status	Published - 1 Jan 2010

Keywords

Inhomogeneous medium
Interior transmission problem
Inverse scattering
Trans-mission eigenvalues

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10.1137/090754637

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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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AU - Cakoni, Fioralba

AU - Colton, David

AU - Haddar, Houssem

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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

U2 - 10.1137/090754637

DO - 10.1137/090754637

M3 - Article

AN - SCOPUS:77954406522

SN - 0036-1410

VL - 42

SP - 145

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

Keywords

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