Geodesic
On Operator Estimates of the Homogenization of Higher-Order Elliptic Systems
Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 370-389

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In the space $\mathbb R^d$, we consider matrix elliptic operators $L_\varepsilon$ of arbitrary even order $2m\ge 4$ with measurable $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. We construct an approximation to the resolvent of this operator with an error of the order of $\varepsilon^2$ in the operator $(L^2\to L^2)$-norm.
Keywords: homogenization, approximation to the resolvent, higher-order elliptic system. 
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     author = {S. E. Pastukhova},
     title = {On {Operator} {Estimates} of the {Homogenization} of {Higher-Order} {Elliptic} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {370--389},
     publisher = {mathdoc},
     volume = {114},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a4/}
}
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S. E. Pastukhova. On Operator Estimates of the Homogenization of Higher-Order Elliptic Systems. Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 370-389. http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a4/