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Full-Text Articles in Physical Sciences and Mathematics
Convergence Rates And Hölder Estimates In Almost-Periodic Homogenization Of Elliptic Systems, Zhongwei Shen
Convergence Rates And Hölder Estimates In Almost-Periodic Homogenization Of Elliptic Systems, Zhongwei Shen
Mathematics Faculty Publications
For a family of second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the coefficients. The results are used to investigate the problem of convergence rates. We also establish uniform Hölder estimates for the Dirichlet problem in a bounded C1,α domain.
Homogenization Of Stokes Systems And Uniform Regularity Estimates, Shu Gu, Zhongwei Shen
Homogenization Of Stokes Systems And Uniform Regularity Estimates, Shu Gu, Zhongwei Shen
Mathematics Faculty Publications
This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as a Liouville property for solutions in ℝd. We also obtain the boundary W1,p estimates in a bounded C1 domain for any 1 < p < ∞.