Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

Jun Geng; Zhongwei Shen; Liang Song

doi:10.1007/s00205-017-1103-6

Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

Jun Geng, Zhongwei Shen, Liang Song

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

10 Scopus citations

Abstract

This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L² boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).

Original language	English
Pages (from-to)	1205-1236
Number of pages	32
Journal	Archive for Rational Mechanics and Analysis
Volume	224
Issue number	3
DOIs	https://doi.org/10.1007/s00205-017-1103-6
State	Published - Jun 1 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

Access to Document

10.1007/s00205-017-1103-6

Cite this

@article{9dac38a2bb994785a1017a775c1cd9be,

title = "Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity",

abstract = "This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).",

author = "Jun Geng and Zhongwei Shen and Liang Song",

note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag Berlin Heidelberg.",

year = "2017",

month = jun,

day = "1",

doi = "10.1007/s00205-017-1103-6",

language = "English",

volume = "224",

pages = "1205--1236",

number = "3",

}

TY - JOUR

T1 - Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

AU - Geng, Jun

AU - Shen, Zhongwei

AU - Song, Liang

PY - 2017/6/1

Y1 - 2017/6/1

N2 - This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).

AB - This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).

UR - http://www.scopus.com/inward/record.url?scp=85014035977&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014035977&partnerID=8YFLogxK

U2 - 10.1007/s00205-017-1103-6

DO - 10.1007/s00205-017-1103-6

M3 - Article

AN - SCOPUS:85014035977

SN - 0003-9527

VL - 224

SP - 1205

EP - 1236

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

ER -

Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this