# American Institute of Mathematical Sciences

August  2012, 6(3): 487-521. doi: 10.3934/ipi.2012.6.487

## The Green function of the interior transmission problem and its applications

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

Received  February 2012 Revised  May 2012 Published  September 2012

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.
Citation: Kyoungsun Kim, Gen Nakamura, Mourad Sini. The Green function of the interior transmission problem and its applications. Inverse Problems & Imaging, 2012, 6 (3) : 487-521. doi: 10.3934/ipi.2012.6.487
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