  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 in
two dimensions. The bow-tie structure consists of two disjoint bounded domains
which have corners with possibly different aperture angles. The domains are
parts of cones near the vertices, and they are nearly touching to each other.
We characterize the field enhancement using explicit functions and, as
consequences, derive optimal estimates of the gradient in terms of the distance
between two inclusions and aperture angles of the corners. The estimates show
that the field is enhanced beyond the corner singularities due to the
interaction between two inclusions.
