  We study periodic homogenization problems for second-order pde in half-space
type domains with Neumann boundary conditions. In particular, we are interested
in "singular problems" for which it is necessary to determine both the
homogenized equation and boundary conditions. We provide new results for fully
nonlinear equations and boundary conditions. Our results extend previous work
of Tanaka in the linear, periodic setting in half-spaces parallel to the axes
of the periodicity, and of Arisawa in a rather restrictive nonlinear periodic
framework. The key step in our analysis is the study of associated ergodic
problems in domains with similar structure.
