M E19

Being motivated the study of negative-index metamaterials, we will discuss the definition and the spectral properties of the operators given by the differential expressions div h grad in a bounded domain U with a function h which is equal to 1 on a part of U and to a constant b<0 on the rest of U. We will see how the properties of such operators depend on the parameter b and on the geometry of U. In particular, one can have a non-empty essential spectrum. Based on a joint work with Claudio Cacciapuoti and Andrea Posilicano (University of Insubria).

Konstantin Pankrashkin

University Paris-Sud