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, ∞ or a finite non-identically vanishing 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 its 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.

我们考虑在具有广义阻抗边角的域中的时谐麦克斯韦系统，即存在两个在边缘相交的广义阻抗平面。阻抗参数可以是0，∞或有限的不相同的消失函数。我们在麦克斯韦系统的解的消失阶与边角的二面角之间建立了精确的关系。特别地，如果角度是不合理的，则消失的顺序是无限的，即，从拐角处保持强烈的唯一连续性。这些新的定量结果的建立涉及高度复杂和微妙的代数论证。独特的连续性研究是由我们对长期存在的逆电磁散射问题的研究所激发的。作为重要的应用，我们通过一次远场测量确定多面体障碍及其表面阻抗，得出了几种新颖的独特可识别性结果。我们还讨论了我们的结果在与信息编码有关的逆散射理论中的另一个潜在的有趣应用。