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arXiv · 2108.01557

Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunction

Hongyu Liu·Chun-Hsiang Tsou
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Abstract

In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability result in determining a polygonal scatterer by a single far-field measurement. The argument in establishing the stability result is localized around a corner and can be as well used to produce two highly intriguing implications for invisibility and transmission resonance in the wave scattering theory. In fact, we show that if a generic medium scatterer possesses an admissible corner on its support, then there exists a positive lower bound of the $L^2$-norm of the associated far-field pattern. For the transmission resonance, we discover a quantitative connection between the regularity of the transmission eigenfunction at a corner and its analytic or Fourier extension.

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Hongyu Liu, Chun-Hsiang Tsou. 2021-08-03. Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunction. https://arxiv.org/abs/2108.01557

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