Establishes transmission eigenvalues with L1 refractive index, suggesting novel insights into wave propagation.
We consider the interior transmission eigenvalue problem \(-u(x)={λ } ρ (x)u(x)\) with the non-selfadjoint boundary conditions \(u(0)=0=u'(1){sin √λ }{√λ }-u(1){cos √λ }\) , where the refractive index \(ρ ∈ L^1\) . We prove the existence of infinitely many transmission eigenvalues. In addition, we show the complete continuity of transmission eigenvalues.
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