  We prove the homogenization of the Dirichlet problem for fully nonlinear
elliptic operators with periodic oscillation in the operator and of the
boundary condition for a general class of smooth bounded domains. This extends
the previous results of Barles and Mironescu in half spaces. We show that
homogenization holds despite a possible lack of continuity in the homogenized
boundary data. The proof is based on a comparison principle with partial
Dirichlet boundary data which is of independent interest.
