Optimal estimates of the field enhancement in presence of a bow-tie structure of perfectly conducting inclusions in two dimensions

摘要

This paper deals with the field enhancement, that is, the gradient blow-up,due to presence of a bow-tie structure of perfectly conducting inclusions intwo dimensions. The bow-tie structure consists of two disjoint bounded domainswhich have corners with possibly different aperture angles. The domains areparts of cones near the vertices, and they are nearly touching to each other.We characterize the field enhancement using explicit functions and, asconsequences, derive optimal estimates of the gradient in terms of the distancebetween two inclusions and aperture angles of the corners. The estimates showthat the field is enhanced beyond the corner singularities due to theinteraction between two inclusions.