  If two conducting or insulating inclusions are closely located, the gradient
of the solution may become arbitrarily large as the distance between inclusions
tends to zero, resulting in high concentration of stress in between two
inclusions. This happens if the bonding of the inclusions and the matrix is
perfect, meaning that the potential and flux are continuous across the
interface. In this paper, we consider the case when the bonding is imperfect.
We consider the case when there are two circular inclusions of the same radii
with the imperfect bonding interfaces and prove that the gradient of the
solution is bounded regardless of the distance between inclusions if the
bonding parameter is finite. This result is of particular importance since the
imperfect bonding interface condition is an approximation of the membrane
structure of biological inclusions such as biological cells.
