A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media

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August 2007, 1(3): 443-456. doi: 10.3934/ipi.2007.1.443

A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media

Fioralba Cakoni ^1, and Houssem Haddar ^2,

1.	Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716-2553
2.	INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France

Received January 2007 Published July 2007

Abstract
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The interior transmission problem plays a basic role in the study of inverse scattering problems for inhomogeneous medium. In this paper we study the interior transmission problem for the Maxwell equations in the electromagnetic scattering problem for an anisotropic inhomogeneous object. We use a variational approach which extends the method developed in [15] to the case when the index of refraction is less than one as well as for partially coated scatterers. In addition, we also describe the structure of the transmission eigenvalues.

Keywords: interior transmission problem; anisotropic media..

Mathematics Subject Classification: Primary: 35R30, 35Q60, 35J40, 78A2.

Citation: Fioralba Cakoni, Houssem Haddar. A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media. Inverse Problems & Imaging, 2007, 1 (3) : 443-456. doi: 10.3934/ipi.2007.1.443

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