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In terms of layer potential methods, this paper is devoted to study the $L^2$boundary value problems for nonhomogeneous elliptic operators with rapidlyoscillating coefficients in a periodic setting. Under a low regularityassumption on the coefficients, we establish the solvability for Dirichlet,regular and Neumann problems in a bounded Lipschitz domain, as well as, theuniform nontangential maximal function estimates and square function estimates.The main difficulty is reflected in two aspects: (i) we can not treat the lowerorder terms as a compact perturbation to the leading term due to the lowregularity assumption; (ii) the nonhomogeneous systems do not possess ascaling-invariant property in general. Although this work may be regarded as afollow-up to C. Kenig and Z. Shen's in \cite{SZW24}, we make an effort to finda clear way of how to handle the nonhomogeneous operators by using the knownresults of the homogenous ones. Also, we mention that the periodicity conditionplays a key role in the scaling-invariant estimates.

The Methods of Layer Potentials for General Elliptic Homogenization Problems in Lipschitz Domains