Combined effects of homogenization and singular perturbations: Quantitative estimates

Weisheng Niu; Zhongwei Shen

doi:10.3233/ASY-211709

Combined effects of homogenization and singular perturbations: Quantitative estimates

Weisheng Niu, Zhongwei Shen

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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	https://doi.org/10.3233/ASY-211709
State	Published - 2022

Bibliographical note

Funding Information:
W. Niu supported by the NSF of China (11971031, 11701002). Z. Shen supported in part by NSF grant DMS-1856235.

Publisher Copyright:
© 2022 - IOS Press. All rights reserved.

Keywords

convergence rate
Homogenization
singular perturbation
uniform Lipschitz estimate

ASJC Scopus subject areas

Mathematics (all)

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10.3233/ASY-211709

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title = "Combined effects of homogenization and singular perturbations: Quantitative estimates",

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 = "convergence rate, Homogenization, singular perturbation, uniform Lipschitz estimate",

author = "Weisheng Niu and Zhongwei Shen",

note = "Funding Information: W. Niu supported by the NSF of China (11971031, 11701002). Z. Shen supported in part by NSF grant DMS-1856235. Publisher Copyright: {\textcopyright} 2022 - IOS Press. All rights reserved.",

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language = "English",

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T1 - Combined effects of homogenization and singular perturbations

T2 - Quantitative estimates

AU - Niu, Weisheng

AU - Shen, Zhongwei

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - convergence rate

KW - Homogenization

KW - singular perturbation

KW - uniform Lipschitz estimate

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DO - 10.3233/ASY-211709

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SN - 0921-7134

VL - 128

SP - 351

EP - 384

JO - Asymptotic Analysis

JF - Asymptotic Analysis

IS - 3

ER -

Combined effects of homogenization and singular perturbations: Quantitative estimates

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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