Quantitative estimates in reiterated homogenization

Weisheng Niu; Zhongwei Shen; Yao Xu

doi:10.1016/j.jfa.2020.108759

Quantitative estimates in reiterated homogenization

Weisheng Niu, Zhongwei Shen, Yao Xu

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

8 Scopus citations

Abstract

This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates down to the finest microscopic scale via iteration and rescaling arguments. We also obtain a convergence rate in the L² space by the reiterated homogenization method.

Original language	English
Article number	108759
Journal	Journal of Functional Analysis
Volume	279
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2020.108759
State	Published - Dec 15 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

Convergence rates
Large-scale regularity estimates
Reiterated homogenization

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2020.108759

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title = "Quantitative estimates in reiterated homogenization",

abstract = "This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates down to the finest microscopic scale via iteration and rescaling arguments. We also obtain a convergence rate in the L2 space by the reiterated homogenization method.",

keywords = "Convergence rates, Large-scale regularity estimates, Reiterated homogenization",

author = "Weisheng Niu and Zhongwei Shen and Yao Xu",

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year = "2020",

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AU - Niu, Weisheng

AU - Shen, Zhongwei

AU - Xu, Yao

PY - 2020/12/15

Y1 - 2020/12/15

N2 - This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates down to the finest microscopic scale via iteration and rescaling arguments. We also obtain a convergence rate in the L2 space by the reiterated homogenization method.

AB - This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates down to the finest microscopic scale via iteration and rescaling arguments. We also obtain a convergence rate in the L2 space by the reiterated homogenization method.

KW - Convergence rates

KW - Large-scale regularity estimates

KW - Reiterated homogenization

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DO - 10.1016/j.jfa.2020.108759

M3 - Article

AN - SCOPUS:85090747298

SN - 0022-1236

VL - 279

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 11

M1 - 108759

ER -

Quantitative estimates in reiterated homogenization

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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