Layer potential methods for elliptic homogenization problems

In this paper we use the method of layer potentials to study L² boundary value problems in a bounded Lipschitz domain Ω for a family of second-order elliptic systems with rapidly oscillating periodic coefficients. Defining, under the assumption that A(X) is elliptic, symmetric, periodic, and Hölder-continuous, we establish the solvability of the L² Dirichlet, regularity, and Neumann problems for in Ω with optimal estimates uniform in ε>0.