Convergence rates and interior estimates in homogenization of higher order elliptic systems

Weisheng Niu; Zhongwei Shen; Yao Xu

doi:10.1016/j.jfa.2018.01.012

Convergence rates and interior estimates in homogenization of higher order elliptic systems

Weisheng Niu, Zhongwei Shen, Yao Xu

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

19 Scopus citations

Abstract

This paper is concerned with the quantitative homogenization of 2m-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp O(ε) convergence rate in W^m−1,p₀ with p₀=[Formula presented] in a bounded Lipschitz domain in R^d as well as the uniform large-scale interior C^m−1,1 estimate. With additional smoothness assumptions, the uniform interior C^m−1,1, W^m,p and C^m−1,α estimates are also obtained. As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions.

Original language	English
Pages (from-to)	2356-2398
Number of pages	43
Journal	Journal of Functional Analysis
Volume	274
Issue number	8
DOIs	https://doi.org/10.1016/j.jfa.2018.01.012
State	Published - Apr 15 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

Convergence rates
Elliptic systems
Higher-order
Homogenization

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2018.01.012

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title = "Convergence rates and interior estimates in homogenization of higher order elliptic systems",

abstract = "This paper is concerned with the quantitative homogenization of 2m-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp O(ε) convergence rate in Wm−1,p0 with p0=[Formula presented] in a bounded Lipschitz domain in Rd as well as the uniform large-scale interior Cm−1,1 estimate. With additional smoothness assumptions, the uniform interior Cm−1,1, Wm,p and Cm−1,α estimates are also obtained. As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions.",

keywords = "Convergence rates, Elliptic systems, Higher-order, Homogenization",

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

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doi = "10.1016/j.jfa.2018.01.012",

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T1 - Convergence rates and interior estimates in homogenization of higher order elliptic systems

AU - Niu, Weisheng

AU - Shen, Zhongwei

AU - Xu, Yao

PY - 2018/4/15

Y1 - 2018/4/15

N2 - This paper is concerned with the quantitative homogenization of 2m-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp O(ε) convergence rate in Wm−1,p0 with p0=[Formula presented] in a bounded Lipschitz domain in Rd as well as the uniform large-scale interior Cm−1,1 estimate. With additional smoothness assumptions, the uniform interior Cm−1,1, Wm,p and Cm−1,α estimates are also obtained. As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions.

AB - This paper is concerned with the quantitative homogenization of 2m-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp O(ε) convergence rate in Wm−1,p0 with p0=[Formula presented] in a bounded Lipschitz domain in Rd as well as the uniform large-scale interior Cm−1,1 estimate. With additional smoothness assumptions, the uniform interior Cm−1,1, Wm,p and Cm−1,α estimates are also obtained. As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions.

KW - Convergence rates

KW - Elliptic systems

KW - Higher-order

KW - Homogenization

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DO - 10.1016/j.jfa.2018.01.012

M3 - Article

AN - SCOPUS:85041596203

SN - 0022-1236

VL - 274

SP - 2356

EP - 2398

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

Convergence rates and interior estimates in homogenization of higher order elliptic systems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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