Abstract
Let Open image in new window ⊂ ℝd be a bounded domain with boundary of class C1,1. In L2( Open image in new window ;ℂn), consider a matrix elliptic second-order differential operator AD,ɛ with Dirichlet boundary condition. Here ɛ > 0 is a small parameter; the coefficients of AD,ɛ are periodic and depend on x/ɛ. The operator AD,ɛ−1 in the norm of operators acting from L2( Open image in new window ;ℂn) to the Sobolev space H1( Open image in new window ;ℂn) is approximated with an error of order ɛ1/2. The approximation is given by the sum of the operator (AD0)−1 and a first-order corrector. Here AD0 is an effective operator with constant coefficients and Dirichlet boundary condition.
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