DOI: 10.1515/jiip-2026-0121 ISSN: 0928-0219

Exterior transmission eigenvalue problem with a piecewise W 2 1 refractive index

Tao Liu, Guangsheng Wei
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Abstract

We study a one-dimensional exterior transmission eigenvalue problem with a piecewise

W 2 1 {W_{2}^{1}}
refractive index. We establish conditions on the refractive index under which the problem has only finitely many real transmission eigenvalues. In addition, we prove that two sets of exterior transmission eigenvalues uniquely determine the refractive index.

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