Improved Resolvent Approximations in Homogenization of Second-Order Operators with Periodic Coefficients

For elliptic divergent self-adjoint second-order operators with \(\varepsilon\)-periodic measurable coefficients acting on the whole space \(\mathbb{R}^d\), resolvent approximations in the operator norm \(\|\!\,\boldsymbol\cdot\,\!\|_{H^1\to H^1}\) with remainder of order \(\varepsilon^2\) as \(\varepsilon\to 0\) are found by the method of two-scale expansions with the use of smoothing.