WIAS Preprint No. 2020, (2014)
Corners and edges always scatter
- Elschner, Johannes
- Hu, Guanghui
2010 Mathematics Subject Classification
- 35R30 78A46
- Helmholtz equation, inverse medium scattering, uniqueness, shape identification, corner and wedge domains
Consider time-harmonic acoustic scattering problems governed by the Helmholtz equation in two and three dimensions. We prove that bounded penetrable obstacles with corners or edges scatter every incident wave nontrivially, provided the function of refractive index is real-analytic. Moreover, if such a penetrable obstacle is a convex polyhedron or polygon, then its shape can be uniquely determined by the far-field pattern over all observation directions incited by a single incident wave. Our arguments are elementary and rely on the expansion of solutions to the Helmholtz equation.
- Inverse Problems, 015003/1--015003/17 (2015) pp. .