# Homogenization of Oscillating Boundary Conditions

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I will discuss the homogenization of periodic oscillating Dirichlet

boundary problems in general domains for second order uniformly elliptic

equations. These problems are connected with the study of boundary layers

in fluid mechanics and with the study of higher order asymptotic expansions

in interior homogenization theory. The talk will be aimed at a general

audience. I will explain some recent progress about the continuity

properties of the homogenized problem which displays a sharp contrast

between the case of linear and nonlinear interior equations. This is based

on joint work with Inwon Kim.