The Existence of an Infinite Discrete Set of Transmission Eigenvalues

Abstract. We prove the existence of an infinite discrete set of transmission eigenvalues corresponding to the scattering problem for isotropic and anisotropic inhomogeneous media for both the Helmholtz and Maxwell's equations. Our discussion includes the case of the interior transmission problem for an inhomogeneous medium with cavities, i.e. subregions with contrast zero. Key words. Interior transmission problem, transmission eigenvalues, inhomogeneous medium, inverse scattering. AMS subject classifications. 35R30, 35Q60, 35J40, 78A25.

• Type: Journal
• Year: 2010
• Where: SIAMMA
• Authors: Fioralba Cakoni, Drossos Gintides, Houssem Haddar
• Keywords: Inhomogeneous Medium, Interior Transmission Problem, SIAMMA 2010, Transmission Eigenvalues