Improved Resolvent Approximations in Homogenization of Second-Order Operators with Periodic Coefficients
Svetlana Evgenievna Pastukhova · Functional Analysis and Its Applications · 2022
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.