Asymptotics and Computation of the Solution to the Conductivity Equation   in the Presence of Adjacent Inclusions with Extreme Conductivities
  When inclusions with extreme conductivity (insulator or perfect conductor) are closely located, the gradient of the solution to the conductivity equation can be arbitrarily large. And computation of the gradient is extremely challenging due to its nature of blow-up in a narrow region in between inclusions. In this paper we characterize explicitly the singular term of the solution when two circular inclusions with extreme conductivities are adjacent. Moreover, we show through numerical computations that the characterization of the singular term can be used efficiently for computation of the gradient in the presence adjacent inclusions. 
Hyeonbae Kang, Mikyoung Lim and KiHyun Yun
math.AP