Weakly singular corners always scatter
Analysis of PDEs
2018-01-15 v1
Abstract
Assume that a bounded scatterer is embedded into an infinite homogeneous isotropic background medium in two dimensions. The refractive index function is supposed to be piecewise constant. If the scattering interface contains a weakly or strongly singular point, we prove that the scattered field cannot vanish identically. This particularly leads to the absence of non-scattering energies for piecewise analytic interfaces with a weakly singular point. Local uniqueness is obtained for shape identification problems in inverse medium scattering with a single far-field pattern.
Cite
@article{arxiv.1801.04037,
title = {Weakly singular corners always scatter},
author = {Long Li and Guanghui Hu and Jiansheng Yang},
journal= {arXiv preprint arXiv:1801.04037},
year = {2018}
}