The Green function of the interior transmission problem and its applications

Kyoungsun Kim; Gen Nakamura; Mourad Sini

doi:10.3934/ipi.2012.6.487

Article Contents

2012, Volume 6, Issue 3: 487-521. Doi: 10.3934/ipi.2012.6.487

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The Green function of the interior transmission problem and its applications

1.
Department of Mathematics of Inha University, Incheon 402-751
2.
Department of Mathematics, Hokkaido University, Sapporo 060-0810
3.
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz A-4040

Received: January 31, 2012

Revised: April 30, 2012

Published: July 2012

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Abstract

The interior transmission problem appears naturally in the scattering theory. In this paper, we construct the Green function associated to this problem. In addition, we provide point-wise estimates of this Green function similar to those known for the Green function related to the classical transmission problems. These estimates are, in particular, useful to the study of various inverse scattering problems. Here, we apply them to justify some asymptotic formulas already used for detecting partially coated dielectric mediums from far field measurements.

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Mathematics Subject Classification: Primary: 35J08, 35J25; Secondary: 35S15.

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