Asymptotics of the solution to the conductivity equation in the presence of an inclusion with eccentric core-shell geometry
Junbeom Kim, Mikyoung Lim · arXiv (Cornell University) · 2017
In this paper, we analyze the gradient blow-up of the solution to the conductivity equation in two dimensions in the presence of an inclusion with eccentric core-shell geometry. We derive an asymptotic approximation for the solution in terms of the single and double layer potentials with line charges, assuming that the core and shell have circular boundaries and the distance between the two boundaries is very small. The integral asymptotic expression explicitly shows the gradient blow-up feature when the core is located nearly touching to the shell's boundary.