In a planar infinite strip with a fast oscillating boundary we consider an
elliptic operator assuming that both the period and the amplitude of the
oscillations are small. On the oscillating boundary we impose Dirichlet,
Neumann or Robin boundary condition. In all cases we describe the homogenized
operator, establish the uniform resolvent convergence of the perturbed
resolvent to the homogenized one, and prove the estimates for the rate of
convergence. These results are obtained as the order of the amplitude of the
oscillations is less, equal or greater than that of the period. It is shown
that under the homogenization the type of the boundary condition can change
