Lipschitz Estimates in Almost-Periodic Homogenization

Armstrong, Scott N.; Shen, Zhongwei

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

Number

Publisher

Interscience Publishers

Published in

Paris

Pages

1882-1923

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