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Physical Sciences and Mathematics Commons

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Mathematics

University of Kentucky

2015

Homogenization

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

Convergence Rates And Hölder Estimates In Almost-Periodic Homogenization Of Elliptic Systems, Zhongwei Shen Sep 2015

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 Jan 2015

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 < ∞.