On the existence of transmission eigenvalues

By Andreas Kirsch. 2009

155 citations recorded by the source corpus.

The investigation of the far field operator and the Factorization Method in inverse scattering theory leads naturally to the study of corresponding interior transmission eigenvalue problems. In contrast to the classical Dirichlet- or Neumann eigenvalue problem for $-\Delta$ in bounded domains these interior transmiision eigenvalue problem fail to be selfadjoint. In general, existence of eigenvalues is an open problem. In this paper we prove existence of eigenvalues for the scalar Helmholtz equation (isotropic and anisotropic cases) and Maxwell's equations under the condition that the contrast of the scattering medium is large enough.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/21634372aa23f65192405179ac1c7a01a574f9f6

How researchers see this paper

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In Computational Theory and Mathematics

1. David Colton
2. Peter B. Monk
3. Fioralba Cakoni
4. Jiguang Sun
5. Annalisa Buffa
6. Snorre H. Christiansen

In Mathematical Physics

1. Fioralba Cakoni
2. David Colton
3. Jiguang Sun
4. Peter B. Monk
5. Andreas Kirsch
6. Houssem Haddar
7. Michele Piana
8. Roland W. E. Potthast

Citations in the corpus

• The inverse electromagnetic scattering problem for anisotropic media (2010, background): “Note that F depends linearly on g and is injective with the dense range provided k is not a transmission eigenvalue [6, 14], i.”
• Analytical and computational methods for transmission eigenvalues (2010, background): “Then 1 n−1 ≥ σ > 0 and following [8] we define Aτ (u, v) = (”