The Interior Transmission Problem for Regions with Cavities

We consider the interior transmission problem in the case when the inhomogeneous medium has cavities, i.e. regions in which the index of refraction is the same as the host medium. In this case we establish the Fredholm property for this problem and show that transmission eigenvalues exist and form a discrete set. We also derive Faber-Krahn type inequalities for the transmission eigenvalues. Key words. Inhomogeneous medium, interior transmission problem, inverse scattering, transmission eigenvalues. AMS subject classifications. 35R30, 35Q60, 35J40, 78A25.

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