Convergence Rates and Hölder Estimates in Almost-Periodic Homogenization of Elliptic Systems

2014/04/23 by Zhongwei Shen, Shen, Zhongwei · 4 citations
Computer Science · Engineering · Mathematics · #35B27 #35J55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #msc:35B27 #msc:35J55

paper · pdf · doi:10.48550/arxiv.1404.5846

41 pages; minor revision of the previous version

openalex publication_date 2014/04/23 · arxiv created 2015/06/24 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 C^{1, α} domain.

Cited by

• Optimal convergence rates in multiscale elliptic homogenization
• Generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost periodic media
• Lipschitz estimates in almost-periodic homogenization
• Convergence Rate of Birkhoff Average for Toral Quasi-Periodic Rotations and Applications

Related

• Approximate Correctors and Convergence Rates in Almost-Periodic Homogenization
• Convergence Rates in Almost-Periodic Homogenization of Higher-order Elliptic Systems
• Uniform Regularity Estimates in Homogenization Theory of Elliptic System with Lower Order terms
• Lipschitz estimates in almost-periodic homogenization
• Lectures on Periodic Homogenization of Elliptic Systems