Transmission eigenvalues

The 2013 special issue of Inverse Problems describes papers that are concerned with the question of existence of transmission eigenvalues and the structure of the associated transmission eigenfunctions. The three papers by respectively Robbiano, Blasten and Päivärinta and Lakshtanov and Vainberg provide newcomplementary results on the existence of transmission eigenvalues for the scalar problem under weak assumptions on the refractive index that mainly stipulates that the contrast does not change sign on the boundary. On the other hand, the paper by Bonnet-Ben Dhia and Chesnel addresses the Fredholm properties of the interior transmission problem when the contrast changes sign on the boundary, exhibiting cases where this property fails. Using more standard approaches, the existence and structure of transmission eigenvalues are analyzed in the paper by Delbary.