Convergence rates in almost-periodic homogenization of higher-order elliptic systems
Yao Xu, Weisheng Niu · Asymptotic Analysis · 2020
This paper concentrates on the quantitative homogenization of higher-order elliptic systems with almost-periodic coefficients in bounded Lipschitz domains. For almost-periodic coefficients in the sense of H. Weyl, we establish uniform local [Formula: see text] estimates for the approximate correctors. Under an additional assumption ( 1.8 ) on the frequencies of the coefficients, we derive the existence of true correctors as well as the [Formula: see text] convergence rate in [Formula: see text]. As a byproduct, the large-scale Hölder estimate and a Liouville theorem are obtained for higher-order elliptic systems with almost-periodic coefficients in the sense of Besicovitch. Since ( 1.8 ) is not well-defined for equivalence classes of almost-periodic functions in the sense of H. Weyl or Besicovitch, we provide another condition yielding the [Formula: see text] convergence rate under perturbations of the coefficients.