论文标题
导电传输本征函数和应用的局部几何特性
Local geometric properties of conductive transmission eigenfunctions and applications
论文作者
论文摘要
纸的目的是双重的。首先，我们表明，与导电边界条件相关的部分数据传输特征函数在$ \ mathbb {r}^n $，$ n = 2,3 $的多面角或圆锥角周围消失。其次，我们将光谱特性应用于确定形状的几何反向散射问题，即通过单个远场测量值确定导电散射器的边界阻抗参数，独立于其培养基。我们建立了几个新的独特恢复结果。结果将相关的结果扩展到两个方向上：首先，我们考虑了一个更通用的几何设置，其中研究了多面体和圆锥角，而在[30]中，仅涉及多面角。其次，我们显着放松[30]中的规律性假设，这对于上面提到的几何逆问题特别有用。我们制定了新的技术策略来实现这些新结果。
The purpose of the paper is twofold. First, we show that partial-data transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in $\mathbb{R}^n$, $n=2,3$. Second, we apply the spectral property to the geometrical inverse scattering problem of determining the shape as well as its boundary impedance parameter of a conductive scatterer, independent of its medium content, by a single far-field measurement. We establish several new unique recovery results. The results extend the relevant ones in [30] in two directions: first, we consider a more general geometric setup where both polyhedral and conic corners are investigated, whereas in [30] only polyhedral corners are concerned; second, we significantly relax the regularity assumptions in [30] which is particularly useful for the geometrical inverse problem mentioned above. We develop novel technical strategies to achieve these new results.
