Blow-up of Electric Fields between Closely Spaced Spherical Perfect Conductors
Mikyoung Lim, KiHyun Yun · Communications in Partial Differential Equations · 2009
The electric field increases toward infinity in the narrow region between closely adjacent perfect conductors as they approach each other. Much attention has been devoted to the blow-up estimate, especially in two dimensions, for the practical relevance to high stress concentration in fiber-reinforced elastic composites. In this paper, we establish optimal estimates for the electric field associated with the distance between two spherical conductors in n-dimensional spaces for n ≥ 2. The novelty of these estimates is that they explicitly describe the dependency of the blow-up rate on the geometric parameters: the radii of the conductors.