Dirichlet Problems In Homogenization Of Second Order Elliptic Systems In Lipschitz Domains

We consider a family of second-order elliptic operators{Lε} in divergence form with rapidly oscillating periodic coefficients in Lipschitz domains.By ap-plying harmonic analysis methods,we show that the Lp Dirichlet problem for second order elliptic systems is uniquely solvable for 2-δ<p<2(n-1)/n-3+δ if n ≥ 4.In scale case we obtain that the W1,p estimate of Dirichlet problem holds for 3/2-δ<p<3+δ,and the range of p is sharp.