Sharp estimate of electric field from a conductive rod and application. Issue 1 (28th October 2020)

• Record Type: Journal Article
• Authors: Fang, Xiaoping; Deng, Youjun; Liu, Hongyu
• Is Part Of: Studies in applied mathematics. Volume 146:Issue 1(2021)
• Page Start: 279
• Page End: 297
• Publication Date: 2020-10-28
• Subjects: asymptotic analysis -- conductivity equation -- electrical impedance tomography -- Neumann–Poincaré operator -- rod inclusion -- single measurement; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12348
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: 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 characterize the localization 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 Calderón's inverse inclusion problem in the literature.