Superlens-cloaking of small dielectric bodies in the quasistatic regime

It has been conjectured that, in the quasistatic regime, dielectric bodies of finite size could be perfectly cloaked by certain cylindrical arrangements of materials of positive and negative permittivities known as superlenses. We show that, although they do not cloak perfectly dielectrics objects of any size, cylindrical superlenses do cloak, to a significant extent, dielectric bodies of small size.