Title: On the interior transmission eigenvalue problem

Authors: Fioralba Cakoni, Andreas Kirsch

Addresses: Department of Mathmatical Sciences, University of Delaware, Newark, Delaware 197167, USA. ' Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany

Abstract: We consider the transmission eigenvalue problem corresponding to the scattering problem for anisotropic media for both the scalar Helmholtz equation and Maxwell|s equations in the case when the contrast in the scattering media occurs in two independent functions. We prove the existence of an infinite discrete set of transmission eigenvalues provided that the two contrasts are of opposite signs. In this case we provide bounds for the first transmission eigenvalue in terms of the ratio of refractive indices. In the case of the same sign contrasts for the scalar case we show the existence of a finite number of transmission eigenvalues under restrictive assumptions on the strength of the scattering media.

Keywords: interior transmission problem; transmission eigenvalues; inhomogeneous medium; inverse scattering.

DOI: 10.1504/IJCSM.2010.033932

International Journal of Computing Science and Mathematics, 2010 Vol.3 No.1/2, pp.142 - 167

Available online: 04 Jul 2010 *

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