Geodesic
Approximation of resolvents in homogenization of fourth-order elliptic operators
Sbornik. Mathematics, Tome 212 (2021) no. 1, pp. 111-134 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the homogenization of a fourth-order divergent elliptic operator $A_\varepsilon$ with rapidly oscillating $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. The homogenized operator $A_0$ is of the same type and has constant coefficients. We apply Zhikov's shift method to obtain an estimate in the $(L^2\to L^2)$-operator norm of order $\varepsilon^2$ for the difference of the resolvents $(A_\varepsilon+1)^{-1}$ and $(A_0+1)^{-1}$. Bibliography: 25 titles.
Keywords: approximation of resolvents, operator estimate of the homogenization error, corrector, shift method, fourth-order elliptic operator. 
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S. E. Pastukhova. Approximation of resolvents in homogenization of fourth-order elliptic operators. Sbornik. Mathematics, Tome 212 (2021) no. 1, pp. 111-134. http://geodesic.mathdoc.fr/item/SM_2021_212_1_a4/

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