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arXiv · 2208.00189

Improved homogenization estimates for high order elliptic systems

Svetlana Pastukhova
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Abstract

In the whole space $R^d$ ($d\ge 2$), we study homogenization of a divergence-form matrix elliptic operator $L_\varepsilon$ of an arbitrary even order larger than 2 with measurable $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. We constuct an approximation for the resolvent of $L_\varepsilon$ with the remainder term of order $\varepsilon^2$ in the operator $L^2$-norm. We impose no regularity conditions on the operator beyond ellipticity and boundedness of coefficients. We use two scale expansions with correctors regularized by the Steklov smoothing.

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Svetlana Pastukhova. 2022-07-30. Improved homogenization estimates for high order elliptic systems. https://arxiv.org/abs/2208.00189

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