New results on transmission eigenvalues | Zendy

Fioralba Cakoni | Zendy; Drossos Gintides | Zendy

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New results on transmission eigenvalues

Author(s) -

Fioralba Cakoni,

Drossos Gintides

Publication year - 2010

Publication title -

inverse problems and imaging

Language(s) - English

Resource type - Journals

eISSN - 1930-8345

pISSN - 1930-8337

DOI - 10.3934/ipi.2010.4.39

Subject(s) - eigenvalues and eigenvectors , isotropy , transmission (telecommunications) , constant (computer programming) , mathematical analysis , upper and lower bounds , refraction , inverse , refractive index , mathematics , eigenvalue perturbation , physics , optics , geometry , quantum mechanics , computer science , telecommunications , programming language

We consider the interior transmission eigenvalue problem corresponding to the inverse scattering problem for an isotropic inhomogeneous medium. We first prove that transmission eigenvalues exist for media with index of refraction greater or less than one without assuming that the contrast is sufficiently large. Then we show that for an arbitrary Lipshitz domain with constant index of refraction there exists an infinite discrete set of transmission eigenvalues that accumulate at infinity. Finally, for the general case of non constant index of refraction we provide a lower and an upper bound for the first transmission eigenvalue in terms of the first transmission eigenvalue for appropriate balls with constant index of refraction. © 2010 American Institute of Mathematical Sciences

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