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Convergence rates and interior estimates in homogenization of higher order elliptic systems. (English) Zbl 1412.35025

In this interesting paper, the authors consider a family of even order elliptic systems dependent on a small positive parameter \(\epsilon\) with rapidly oscillating periodic coefficients, posed on a bounded Lipschitz domain in \(\mathbb{R}^d\) with a Dirichlet boundary condition.
First, an optimal rate of convergence is established, as \(\epsilon\) tends to zero, for the solution of the initial problem to the solution of a homogenized one. Moreover, interior uniform estimates, and a uniform regularity result for the quantitative homogenization of higher-order elliptic systems of this kind are proven. The derived regularity estimates are applied to the construction of asymptotic expansions of the fundamental solutions.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J58 Boundary value problems for higher-order elliptic systems
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
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References:

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