  This paper deals with the homogenization of a mixed boundary value problem
for the Laplace operator in a domain with locally periodic oscillating
boundary. The Neumann condition is prescribed on the oscillating part of the
boundary, and the Dirichlet condition on a separate part. It is shown that the
homogenization result holds in the sense of weak $L^2$ convergence of the
solutions and their flows, under natural hypothesis on the regularity of the
domain. The strong $L^2$ convergence of average preserving extensions of the
solutions and their flows is also considered.
