Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunction
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 -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.
Cite
@article{arxiv.2108.01557,
title = {Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunction},
author = {Hongyu Liu and Chun-Hsiang Tsou},
journal= {arXiv preprint arXiv:2108.01557},
year = {2022}
}