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arXiv · 2005.06352

Unique continuation from a generalized impedance edge-corner for Maxwell's system and applications to inverse problems

Huaian Diao·Hongyu Liu·Long Zhang·Jun Zou
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Abstract

We consider the time-harmonic Maxwell system in a domain with a generalized impedance edge-corner, namely the presence of two generalized impedance planes that intersect at an edge. The impedance parameter can be $0, \infty$ or a finite non-identically vanishing variable function. We establish an accurate relationship between the vanishing order of the solutions to the Maxwell system and the dihedral angle of the edge-corner. In particular, if the angle is irrational, the vanishing order is infinity, i.e. strong unique continuation holds from the edge-corner. The establishment of those new quantitative results involve a highly intricate and subtle algebraic argument. The unique continuation study is strongly motivated by our study of a longstanding inverse electromagnetic scattering problem. As a significant application, we derive several novel unique identifiability results in determining a polyhedral obstacle as well as it surface impedance by a single far-field measurement. We also discuss another potential and interesting application of our result in the inverse scattering theory related to the information encoding.

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Huaian Diao, Hongyu Liu, Long Zhang, Jun Zou. 2020-05-14. Unique continuation from a generalized impedance edge-corner for Maxwell's system and applications to inverse problems. https://arxiv.org/abs/2005.06352

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