Unique continuation from a generalized impedance edge-corner for Maxwell's system and applications to inverse problems
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 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.
Cite
@article{arxiv.2005.06352,
title = {Unique continuation from a generalized impedance edge-corner for Maxwell's system and applications to inverse problems},
author = {Huaian Diao and Hongyu Liu and Long Zhang and Jun Zou},
journal= {arXiv preprint arXiv:2005.06352},
year = {2020}
}