On Operator Estimates of the Homogenization of Higher-Order Elliptic Systems
Svetlana Evgenievna Pastukhova · Mathematical Notes · 2023
In the space $$\mathbb R^d$$ , we consider matrix elliptic operators $$L_\varepsilon$$ of arbitrary even order $$2m\ge 4$$ with measurable $$\varepsilon$$ -periodic coefficients, where $$\varepsilon$$ is a small parameter. We construct an approximation to the resolvent of this operator with an error of the order of $$\varepsilon^2$$ in the operator $$(L^2\to L^2)$$ -norm.