The Interior Transmission Eigenvalue Problem for Absorbing Media ‡
نویسنده
چکیده
In the recent years the transmission eigenvalue problem has been extensively studied for non-absorbing media. In this paper we initiate the study of this problem for absorbing media. In particular we show that, in the case of absorbing media, transmission eigenvalues form a discrete set, exist for sufficiently small absorption and for spherically stratified media exist without this assumption. For constant index of refraction we also obtain regions in the complex plane where the transmission eigenvalues cannot exist and obtain a priori estimate for real transmission eigenvalues.
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