  This paper deals with the homogenization of fully nonlinear second order
equation with an oscillating Dirichlet boundary data when the operator and
boundary data are $\e$-periodic. We will show that the solution $u_\e$
converges to some function $\bar u(x)$ uniformly on every compact subset $K$ of
the domain $D$. Moreover, $\bar u$ is a solution to some boundary value
problem. For this result, we assume that the boundary of the domain has no
(rational) flat spots and the ratio of elliptic constants $\Lambda / \lambda$
is sufficiently large.
