The Interior Transmission Eigenvalue Problem

We consider the inverse problem of determining the spherically symmetric index of refraction n(r) from a knowledge of the corresponding transmission eigenvalues (which can be determined from field pattern of the scattered wave). We also show that for constant index of refraction n(r) = n, the smallest transmission eigenvalue suffices to determine n, complex eigenvalues exist for n sufficiently small and, for homogeneous media of general shape, determine a region in the complex plane where complex eigenvalues must lie. 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, David Colton, Drossos Gintides
• Keywords: Complex Eigenvalues, Corresponding Transmission Eigenvalues, SIAMMA 2010, Transmission Eigenvalues