We consider second order elliptic operator with ε-periodic measurable coefficients in divergence form, acting in the space ℝd. For the resolvent of this operator we construct approximations in the operator norm \( {\left\Vert \cdot \right\Vert}_{H^1\to {L}^2} \) with the remainder of order ε3 as ε → 0.
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Translated from Problemy Matematicheskogo Analiza 117, 2022, pp. 85-97.
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Pastukhova, S.E. Approximations of Resolvents of Second Order Elliptic Operators with Periodic Coefficients. J Math Sci 267, 382–397 (2022). https://doi.org/10.1007/s10958-022-06141-y
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DOI: https://doi.org/10.1007/s10958-022-06141-y