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arXiv · 1801.04037

Weakly singular corners always scatter

Long Li·Guanghui Hu·Jiansheng Yang
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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.

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Long Li, Guanghui Hu, Jiansheng Yang. 2018-01-12. Weakly singular corners always scatter. https://arxiv.org/abs/1801.04037

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