ALMOST-PERIODIC HOMOGENIZATION OF ELLIPTIC PROBLEMS IN NON-SMOOTH DOMAINS

We consider a family of second-order elliptic operators {L-epsilon} in divergence form with rapidly oscillating and almost-periodic coefficients in Lipschitz domains. By using the compactness method, we show that the uniform W-1,W- p estimate of second-order elliptic systems holds for 2n/n+1 -delta < p < 2n/n-1 + delta; the ranges are sharp for n = 2 or n = 3. In the scalar case we obtain that the W-1,W- p estimate holds for 3/2 - delta < p < 3 + delta if n >= 3, and 4/3 - delta < p < 4 + delta if n = 2; the ranges of p are sharp.