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Lipschitz Estimates in Almost-Periodic Homogenization

Armstrong, Scott N.; Shen, Zhongwei (2016), Lipschitz Estimates in Almost-Periodic Homogenization, Communications on Pure and Applied Mathematics, 69, 10, p. 1882-1923. 10.1002/cpa.21616

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1409.2094v2
Date
2016
Journal name
Communications on Pure and Applied Mathematics
Volume
69
Number
10
Publisher
Interscience Publishers
Published in
Paris
Pages
1882-1923
Publication identifier
10.1002/cpa.21616
Metadata
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Author(s)
Armstrong, Scott N.

Shen, Zhongwei
Abstract (EN)
We establish uniform Lipschitz estimates for second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients. We give interior estimates as well as estimates up to the boundary in bounded C1,α domains with either Dirichlet or Neumann data. The main results extend those in the periodic setting due to Avellaneda and Lin for interior and Dirichlet boundary estimates and later Kenig, Lin, and Shen for the Neumann boundary conditions. In contrast to these papers, our arguments are constructive (and thus the constants are in principle computable) and the results for the Neumann conditions are new even in the periodic setting, since we can treat nonsymmetric coefficients. We also obtain uniform W1,p estimates
Subjects / Keywords
almost-periodic coefficients; Lipschitz estimates; homogenization

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