Uniqueness for inverse elastic scattering from general obstacles with a single incident wave

Establish uniqueness for the inverse elastic scattering problem for general obstacles from the far-field pattern generated by a single incident elastic plane wave, without imposing additional geometric assumptions on the obstacle.

Background

The paper studies inverse time-harmonic elastic scattering by bounded, traction-free polygonal obstacles in two dimensions. Its main theorem proves that a connected polygonal obstacle is uniquely determined by one complete far-field pattern corresponding to a fixed incident direction and frequency. The proof relies on a reflection principle for the Navier equation under traction-free boundary conditions and analytic continuation across polygonal edges and corners.

The authors place this result within the broader unresolved problem of single-wave inverse scattering for general elastic obstacles. Existing uniqueness results are available only for special geometries or boundary conditions, such as rigid balls, convex polyhedra, or selected exterior boundary-value problems. Thus, extending single-incident-wave uniqueness beyond the polygonal and otherwise specially structured settings remains open.