We are concerned with the quantitative study of the electric field perturbation due to the presence of an inhomogeneous conductive rod embedded in a homogenous conductivity. We sharply quantify the dependence of the perturbed electric field on the geometry of the conductive rod. In particular, we accurately characterise the localisation of the gradient field (i.e. the electric current) near the boundary of the rod where the curvature is sufficiently large. We develop layer-potential techniques in deriving the quantitative estimates and the major difficulty comes from the anisotropic geometry of the rod.The result complements and sharpens several existing studies in the literature. It also generates an interesting application in EIT (electrical impedance tomography) in determining the conductive rod by a single measurement, which is also known as the Calderon's inverse inclusion problem in the literature.

中文翻译：

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导电棒电场的精确估计及其应用

由于存在嵌入均匀导电性的非均匀导电棒，我们关注电场扰动的定量研究。我们清晰地量化了扰动电场对导电棒几何形状的依赖性。特别是，我们准确地表征了曲率足够大的棒边界附近的梯度场（即电流）的定位。我们开发了层电位技术来推导定量估计，主要困难来自杆的各向异性几何形状。结果补充并加强了文献中的几项现有研究。它还在 EIT（电阻抗断层扫描）中产生了一个有趣的应用，即通过单次测量确定导电棒，