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.
| Original language | English |
|---|---|
| Pages (from-to) | 351-384 |
| Number of pages | 34 |
| Journal | Asymptotic Analysis |
| Volume | 128 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022 - IOS Press. All rights reserved.
Funding
W. Niu supported by the NSF of China (11971031, 11701002). Z. Shen supported in part by NSF grant DMS-1856235.
| Funders | Funder number |
|---|---|
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China | DMS-1856235 |
| National Natural Science Foundation of China (NSFC) | 11971031, 11701002 |
Keywords
- Homogenization
- convergence rate
- singular perturbation
- uniform Lipschitz estimate
ASJC Scopus subject areas
- General Mathematics