  We analyze the behavior of solutions of the Poisson equation with homogeneous
Neumann boundary conditions in a two-dimensional thin domain which presents
locally periodic oscillations at the boundary. The oscillations are such that
both the amplitude and period of the oscillations may vary in space. We obtain
the homogenized limit problem and a corrector result by extending the unfolding
operator method to the case of locally periodic media. We emphasize the fact
that the techniques developed in this paper can be adapted to other locally
periodic cases like reticulated or perforated domains where the period may be
space-dependent.
