Almost-periodic Homogenization Of Elliptic Problems In Non-smooth Domains

We consider a family of second-order elliptic operators{Lε} in divergence form with rapidly oscillating and almost periodic coefficients in Lipschitz domain-s.By using the compactness method,we show that the uniform W1,p estimate of second order elliptic systems holds for,the ranges are sharp for n= 2 or n = 3.In scale case we obtain that the W1,p estimate holds for and;the ranges of p are sharp.