Combined effects of homogenization and singular perturbations: Quantitative estimates

Article type: Research Article

Authors: Niu, Weisheng^a | Shen, Zhongwei^{b; *}

Affiliations: [a] School of Mathematical Science, Anhui University, Hefei, 230601, China | [b] Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, USA

Correspondence: [*] Corresponding author. E-mail: zshen2@uky.edu.

Abstract: We investigate quantitative estimates in periodic homogenization of second-order elliptic systems of elasticity with singular fourth-order perturbations. The convergence rates, which depend on the scale κ that represents the strength of the singular perturbation and on the length scale ε of the heterogeneities, are established. We also obtain the large-scale Lipschitz estimate, down to the scale ε and independent of κ. This large-scale estimate, when combined with small-scale estimates, yields the classical Lipschitz estimate that is uniform in both ε and κ.

Keywords: Homogenization, singular perturbation, convergence rate, uniform Lipschitz estimate

DOI: 10.3233/ASY-211709

Journal: Asymptotic Analysis, vol. 128, no. 3, pp. 351-384, 2022