  We consider degenerate Monge-Ampere equations of the type $$\det D^2 u= f
\quad \{in $\Om$}, \quad \quad f \sim \, d_{\p \Om}^\alpha \quad \{near $\p
\Om$,}$$ where $d_{\p \Om}$ represents the distance to the boundary of the
domain $\Om$ and $\alpha>0$ is a positive power. We obtain $C^2$ estimates at
the boundary under natural conditions on the boundary data and the right hand
side. Similar estimates in two dimensions were obtained by J.X. Hong, G. Huang
and W. Wang.
