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Improved Resolvent Approximations in Homogenization of Second-Order Operators with Periodic Coefficients

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Functional Analysis and Its Applications Aims and scope

Abstract

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.

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Authors and Affiliations

  1. MIREA—Russian Technological University, Moscow, Russia

    S. E. Pastukhova

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

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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2022, Vol. 56, pp. 93–104 https://doi.org/10.4213/faa4010.

Translated by S. E. Pastukhova

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Pastukhova, S.E. Improved Resolvent Approximations in Homogenization of Second-Order Operators with Periodic Coefficients. Funct Anal Its Appl 56, 310–319 (2022). https://doi.org/10.1134/S0016266322040086

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  • DOI: https://doi.org/10.1134/S0016266322040086

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