On the existence of transmission eigenvalues in an inhomogeneous medium

Fioralba Cakoni (1) , Houssem Haddar (2)

1 Department of Mathematical Sciences
2 DeFI - Shape reconstruction and identification

We prove the existence of transmission eigenvalues corresponding to the inverse scattering problem for isotropic and anisotropic media for both scalar Helmholtz equation and Maxwell's equations. Considering a generalized abstract eigenvalue problem, we are able to extend the ideas of Päivärinta and Sylvester to prove the existence of transmission eigenvalues for a larger class of interior transmission problems. Our analysis includes both the case of a medium with positive contrast and of a medium with negative contrast provided that this contrast is large enough.

Mots clés: Interior transmission problem; transmission eigenvalues; inhomogeneous medium; inverse scattering

Domaines: Analyse fonctionnelle [math.FA]; Mathématiques générales [math.GM]

Fioralba Cakoni, Houssem Haddar. On the existence of transmission eigenvalues in an inhomogeneous medium. [Research Report] RR-6779, INRIA. 2008, pp.24. ⟨inria-00347840⟩