On the uniqueness of the inverse elastic scattering problem for periodic structures
eigenvalue problem for the Lamé operator
The authors study the inverse scattering problem to determine the shape of the periodic structure from measurements of the scattered elastic waves on a line above the structure. They derive a uniqueness result of Schiffer's type, i.e. the structure is uniquely determined if the scattered wave is known for a whole interval of frequencies. The main step in the proof is the investigation of an eigenvalue problem for the Lamé operator in a layer which is bounded from below and above by periodic functions.
scientific article; zbMATH DE number 1713410