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

Mathematics

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

7 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

Funding Information:
J. Geng: Supported in part by the NNSF of China (No. 11571152) and Fundamental Research Funds for the Central Universities (2017.01-2018.06).

Funding Information:
L. Song: Supported in part by the NNSF of China (Nos. 11471338 and 11622113) and Guangdong Natural Science Funds for Distinguished Young Scholar (No. 2016A030306040).

Funding Information:
Z. Shen: Supported in part by NSF Grant DMS-1600520.

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

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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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",

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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).

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

Abstract

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