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 the scalar problem and Maxwell's equations. Considering a generalized abstract eigenvalue problem, we are able to extend the ideas of Päivärinta and Sylvester [Transmission eigenvalues, SIAM J. Math. Anal. 40, (2008) pp. 783-753] 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 the contrasts are large enough.

Domaines: Equations aux dérivées partielles [math.AP]

Fioralba Cakoni, Houssem Haddar. On the existence of transmission eigenvalues in an inhomogeneous medium. Applicable Analysis, 2009, 88 (4), pp.475-493. ⟨10.1080/00036810802713966⟩. ⟨hal-00743824⟩