论文标题
从导电杆和应用中对电场的清晰估计
Sharp estimate of electric field from a conductive rod and application
论文作者
论文摘要
由于存在嵌入在同质电导率中的不均匀导电杆，我们关注的是电场扰动的定量研究。我们急剧量化了扰动电场对导电杆几何形状的依赖性。特别是，我们准确地表征了弯曲杆边界附近梯度场（即电流）的定位，其中曲率足够大。我们开发了层势技术来得出定量估计值，主要困难来自杆的各向异性几何形状。结果补充并培养了文献中的一些现有研究。它还在通过单个测量值确定导电杆时在EIT（电阻抗断层扫描）中产生了一个有趣的应用，该测量也称为Calderon在文献中的反向纳入问题。
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.
