  We develop a theory for the interactions between magnetic impurities in
nanoscopic systems. The case of impurities in quantum corrals built on the
(111) Cu surface is analyzed in detail. For elliptical corrals with one
impurity, clear magnetic mirages are obtained. This leads to an enhancement of
the inter-impurity interactions when two impurities are placed at special
points in the corral. We discuss the enhancement of the conduction electron
response to the local perturbation in other nanoscopic systems.
