导电杆电场的精确估计及其应用
Sharp estimate of electric field from a conductive rod and application
摘要：
我们关注的是由于存在嵌入在均匀导电性的非均匀导电杆的电场扰动的定量研究。我们急剧量化的导电棒的几何形状上的扰动电场的依赖性。特别是，我们准确地定位的梯度场（即电流）附近的边界的曲率足够大的杆。我们发展了层势技术来获得定量估计，主要困难来自于杆的各向异性几何形状。它也产生了一个有趣的应用EIT（电阻抗断层扫描）在确定导电杆通过一个单一的测量，这也被称为卡尔德龙的逆包含问题的文献。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
