  In this article we investigate averaging properties of fully nonlinear PDEs
in bounded domains with oscillatory Neumann boundary data. The oscillation is
periodic and is present both in the operator and in the Neumann data. Our main
result states that, when the domain does not have flat boundary parts and when
the homogenized operator is rotation invariant, the solutions uniformly
converge to the homogenized solution solving a Neumann boundary problem.
Furthermore we show that the homogenized Neumann data is continuous with
respect to the normal direction of the boundary.
