Transmission Eigenvalues in Inverse Scattering Theory

Fioralba Cakoni (1) , Houssem Haddar (2)

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

This survey aims to present the state of the art of research on the transmission eigenvalue problem focussing on three main topics, namely the discreteness of transmission eigenvalues, the existence of trans- mission eigenvalues and estimates on transmission eigenvalues, in particular, Faber-Krahn type inequalities.

Domaines: Equations aux dérivées partielles [math.AP]

Fioralba Cakoni, Houssem Haddar. Transmission Eigenvalues in Inverse Scattering Theory. Gunther Uhlmann. Inside Out II, 60, MSRI Publications, pp.527-578, 2012. ⟨hal-00741615⟩