The asymptotics for the perfect conductivity problem with stiff C1,-inclusions
Xia Hao, Zhiwen Zhao · Journal of Mathematical Analysis and Applications · 2021
This paper is devoted to an investigation of blow-up phenomena occurring in high-contrast fiber-reinforced composites. When the distance between perfect conductors or between the conductors and the matrix boundary tends to zero, the electric field may appear blow-up. The major objective of this paper is to give a precise description for the singular behavior of such a high concentration in the presence of C1,α-inclusions with extreme conductivities. Our results contain the boundary and interior asymptotics of the concentrated field in all dimensions. In particular, the blow-up factor for each dimension is accurately captured.