  We study impurity healing effects in models of strongly correlated
superconductors. We show that in general both the range and the amplitude of
the spatial variations caused by nonmagnetic impurities are significantly
suppressed in the superconducting as well as in the normal states. We
explicitly quantify the weights of the local and the non-local responses to
inhomogeneities and show that the former are overwhelmingly dominant over the
latter. By quantifying the spatial range of the local response, we show that it
is restricted to only a few lattice spacings over a significant range of
dopings in the vicinity of the Mott insulating state. We demonstrate that this
healing effect is ultimately due to the suppression of charge fluctuations
induced by Mottness. We also define and solve analytically a simplified yet
accurate model of healing, within which we obtain simple expressions for
quantities of direct experimental relevance.
