Convergence Rates in AlmostPeriodic Homogenization of Higherorder Elliptic Systems
Abstract
This paper concentrates on the quantitative homogenization of higherorder elliptic systems with almostperiodic coefficients in bounded Lipschitz domains. For coefficients which are almostperiodic in the sense of H. Weyl, we establish uniform ocal $L^2$ estimates for the approximate correctors. Under an additional assumption on the frequencies of the coefficients (see (1.10)), we derive the existence of the true correctors as well as the sharp $O(\varepsilon)$ convergence rate in $H^{m1}$. As a byproduct, the largescale Hölder estimate and a Liouville theorem are obtained for higherorder elliptic systems with almostperiodic coefficients in the sense of Besicovish. Since (1.10) is not welldefined for the equivalence classes of almostperiodic functions in the sense of H. Weyl or Besicovish, we provide another condition that implies the sharp convergence rate in terms of perturbations on the coefficients.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 arXiv:
 arXiv:1712.01744
 Bibcode:
 2017arXiv171201744X
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 34 pages