Improved resolvent approximations in homogenization of second order operators with periodic coefficients

S. E. Pastukhova

Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 4, pp. 93-104.

Résumé

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.

Détail

Keywords: periodic differential operators, homogenization, correctors, resolvent approximations, operator error estimates.

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