Quantitative analysis for rod‐shaped inclusion in three‐dimensional conductivity problem

We show a quantitative analysis of the perturbed electric field of a 3D anisotropic conductive rod geometry embedded in homogeneous background, which is an extension of the work in 2D case. The solution to the perturbed problem is presented by layer potential techniques, and dedicated asymptotic analysis is employed for characterization of the density function. The asymptotic result shows that near the high curvature boundary of the rod, the electric field is much strong, compared with other parts adjacent to the rod.