Electric field concentration in the presence of an inclusion with eccentric core-shell geometry

2017/12/21 by Junbeom Kim, Mikyoung Lim, Kim, Junbeom +1 · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems #math.AP

paper · pdf · doi:10.48550/arxiv.1712.07768

32 pages

openalex publication_date 2017/12/21 · arxiv created 2018/05/22 · arxiv updated 2018/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we analyze the gradient blow-up of the solution to the conductivity problem in two dimensions in the presence of an inclusion with eccentric core-shell geometry. Assuming that the core and shell have circular boundaries that are nearly touching, we derive an asymptotic formula for the solution in terms of the single and double layer potentials with image line charges. We also deduce an integral formula with image line charges for the problem relating to two nearly touching separated conductors.

Cited by

• The analysis of resonant frequencies and blow-up estimates of close-to-touching subwavelength resonators in the two-dimensional Helmholtz system
• Resonant frequencies distribution for multiple closely spaced subwavelength resonators
• The convexity of inclusions and gradient's concentration for Lamé systems with partially infinite coefficients
• Mathematical analysis of subwavelength resonant acoustic scattering in multi-layered high-contrast structures

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