Geodesic
Improved resolvent approximations in homogenization of second order operators with periodic coefficients
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 4, pp. 93-104

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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.
Keywords: periodic differential operators, homogenization, correctors, resolvent approximations, operator error estimates. 
@article{FAA_2022_56_4_a7,
     author = {S. E. Pastukhova},
     title = {Improved resolvent approximations in homogenization of second order operators with periodic coefficients},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {93--104},
     publisher = {mathdoc},
     volume = {56},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_4_a7/}
}
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S. E. Pastukhova. Improved resolvent approximations in homogenization of second order operators with periodic coefficients. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 4, pp. 93-104. http://geodesic.mathdoc.fr/item/FAA_2022_56_4_a7/