Piecewise-analytic interfaces with weakly singular points of arbitrary order always scatter

Long Li; Guanghui Hu; Jiansheng Yang

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arXiv · 2010.00748

Piecewise-analytic interfaces with weakly singular points of arbitrary order always scatter

Long Li·Guanghui Hu·Jiansheng Yang

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Abstract

It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always radiates acoustic waves. These results imply the absence of non-scattering energies and non-radiating sources in a domain that is not $C^\infty$-smooth. Local uniqueness results with a single far-field pattern are obtained for inverse source and inverse medium scattering problems. Our arguments provide a sufficient condition of the surface under which solutions to the Helmholtz equation admits no analytical continuation.

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Long Li, Guanghui Hu, Jiansheng Yang. 2020-10-02. Piecewise-analytic interfaces with weakly singular points of arbitrary order always scatter. https://arxiv.org/abs/2010.00748

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