= Boundary corrector in periodic homogenization
{title2=$b^\epsilon|_{\partial\Omega}=-\epsilon w_j(x/\epsilon)\partial_j u_0$}
A bulk cell expansion generally leaves an oscillatory Dirichlet mismatch. A boundary corrector can solve the homogeneous oscillatory conductivity equation with boundary data cancelling that mismatch. It restores the prescribed physical boundary <trace> while leaving the leading bulk cell formula unchanged. Estimates depend on boundary regularity and on the coefficient assumptions.
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