Boundary Layers in Periodic Homogenization of Neumann Problems

Zhongwei Shen; Jinping Zhuge

doi:10.1002/cpa.21740

Boundary Layers in Periodic Homogenization of Neumann Problems

Zhongwei Shen
, Jinping Zhuge

Producción científica: Article › revisión exhaustiva

15 Citas (Scopus)

Resumen

This paper is concerned with a family of second-order elliptic systems in divergence form with rapidly oscillating periodic coefficients. We initiate the study of homogenization and boundary layers for Neumann problems with first-order oscillating boundary data. We identify the homogenized system and establish the sharp rate of convergence in L² in dimension three or higher. Regularity estimates are also obtained for the homogenized boundary data in both Dirichlet and Neumann problems. The results are used to establish a higher-order convergence rate for Neumann problems with nonoscillating data.

Idioma original	English
Páginas (desde-hasta)	2163-2219
Número de páginas	57
Publicación	Communications on Pure and Applied Mathematics
Volumen	71
N.º	11
DOI	https://doi.org/10.1002/cpa.21740
Estado	Published - nov 2018

Nota bibliográfica

Publisher Copyright:
© 2018 Wiley Periodicals, Inc.

Financiación

Acknowledgment. Zhongwei Shen is supported in part by National Science Foundation Grant DMS-1600520. Jinping Zhuge is supported in part by National Science Foundation Grant DMS-1161154. Zhongwei Shen thanks David G\u00E9rard-Varet for bringing the problem of homogenization of the Neumann problem (1.1) to his attention.

Financiadores	Número del financiador
???publication-publication-funding-organisation-not-added???	1161154
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-1600520, DMS-1161154

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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AB - This paper is concerned with a family of second-order elliptic systems in divergence form with rapidly oscillating periodic coefficients. We initiate the study of homogenization and boundary layers for Neumann problems with first-order oscillating boundary data. We identify the homogenized system and establish the sharp rate of convergence in L2 in dimension three or higher. Regularity estimates are also obtained for the homogenized boundary data in both Dirichlet and Neumann problems. The results are used to establish a higher-order convergence rate for Neumann problems with nonoscillating data.

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Boundary Layers in Periodic Homogenization of Neumann Problems

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