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On Operator Estimates of the Homogenization of Higher-Order Elliptic Systems

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Abstract

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.

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Authors and Affiliations

  1. MIREA – Russian Technological University, Moscow, 119454, Russia

    S. E. Pastukhova

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  1. S. E. Pastukhova
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Correspondence to S. E. Pastukhova.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 370–389 https://doi.org/10.4213/mzm14045.

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Pastukhova, S.E. On Operator Estimates of the Homogenization of Higher-Order Elliptic Systems. Math Notes 114, 322–338 (2023). https://doi.org/10.1134/S0001434623090055

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