论文标题
可见性，隐形性和圆锥形奇异性反电磁问题的独特恢复
Visibility, invisibility and unique recovery of inverse electromagnetic problems with conical singularities
论文作者
论文摘要
在本文中，我们在两种情况下研究了时间谐波的电磁散射，在这种情况下，异常的散射器是一对电磁源或不均匀培养基，都具有紧凑的支撑。我们主要关注通过单个远场测量的几何反向散射问题，即恢复散射器的支撑，独立于其物理内容。假定散射器的支撑（本地）具有圆锥形的奇异性。当发生隐形/透明度时，我们建立了散射器的局部表征，表明其特征参数必须在圆锥点周围局部消失。使用这种表征，我们为上述逆散射问题建立了几个局部和全局唯一性结果，表明可见性必须意味着独特的恢复。在此过程中，我们还建立了在Hölder规律性下的圆锥形点附近电磁透射特征功能或根据HERGLOTZ近似方面的规律性条件的局部消失特性。
In this paper, we study time-harmonic electromagnetic scattering in two scenarios, where the anomalous scatterer is either a pair of electromagnetic sources or an inhomogeneous medium, both with compact supports. We are mainly concerned with the geometrical inverse scattering problem of recovering the support of the scatterer, independent of its physical contents, by a single far-field measurement. It is assumed that the support of the scatterer (locally) possesses a conical singularity. We establish a local characterisation of the scatterer when invisibility/transparency occurs, showing that its characteristic parameters must vanish locally around the conical point. Using this characterisation, we establish several local and global uniqueness results for the aforementioned inverse scattering problems, showing that visibility must imply unique recovery. In the process, we also establish the local vanishing property of the electromagnetic transmission eigenfunctions around a conical point under the Hölder regularity or a regularity condition in terms of Herglotz approximation.
