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Uniform Lipschitz Estimates of Homogenization of Elliptic Systems in Divergence Form with Dini Conditions

Uniform Lipschitz Estimates of Homogenization of Elliptic Systems in Divergence Form with Dini... The paper is devoted to the homogenization of elliptic systems in divergence form. We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1, γ domain when the coefficients are Dini continuous, inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives. The results extend Avellaneda and Lin’s work [Comm. Pure Appl. Math., 40: 803–847 (1987)], where H¨older continuity is the main assumption on smoothness of the data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Uniform Lipschitz Estimates of Homogenization of Elliptic Systems in Divergence Form with Dini Conditions

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Publisher
Springer Journals
Copyright
Copyright © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2021
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-021-1001-4
Publisher site
See Article on Publisher Site

Abstract

The paper is devoted to the homogenization of elliptic systems in divergence form. We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1, γ domain when the coefficients are Dini continuous, inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives. The results extend Avellaneda and Lin’s work [Comm. Pure Appl. Math., 40: 803–847 (1987)], where H¨older continuity is the main assumption on smoothness of the data.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 6, 2021

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