Improved Homogenization Estimates for Higher-order Elliptic Operators in Energy Norms
Svetlana Evgenievna Pastukhova · Lobachevskii Journal of Mathematics · 2024
In the space $$\mathbb{R}^{d}$$ , $$d\geq 2$$ , we consider divergence form matrix differential operators $$L_{\varepsilon}$$ of elliptic type and arbitrary even order $$2m\geq 4$$ with measurable $$\varepsilon$$ -periodic coefficients, where $$\varepsilon$$ is a small parameter. We construct resolvent approximations for these operators with an error of the order of $$\varepsilon^{2}$$ in the energy operator $$(L^{2}\to H^{m})$$ -norm.