Mikyoung Lim, mikyoung.lim@gmail.com
Co-authors: Sanghyeon Yu
Asymptotics of the solution to the conductivity equation in the presence of adjacent circular inclusions
We consider the conductivity problem in the presence of adjacent circular inclusions having arbitrary constant
conductivity. When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient
of the solution can be arbitrary large. We characterize the gradient blow-up by deriving an explicit formula
for the singular term of the solution in terms of the Lerch transcendent function. This derivation is valid for
inclusions having arbitrary constant conductivity. We illustrate our results with numerical calculations.