Convergence rates for general elliptic homogenization problems in a bounded Lipschitz domain

2015/12/15 by Qiang Xu, Xu, Qiang
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1512.04632

openalex publication_date 2015/12/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The paper extends the results obtained by C. Kenig, F. Lin and Z. Shen in \citeSZW2 to more general elliptic homogenization problems in two perspectives: lower order terms in the operator and no smoothness on the coefficients. We do not repeat their arguments. Instead we find the new weighted-type estimates for the smoothing operator at scale ε, and combining some techniques developed by Z. Shen in \citeSZW12 leads to our main results. In addition, we also obtain sharp O(ε) convergence rates in L^p with p=2d/(d-1), which were originally established by Z. Shen for elasticity systems in \citeSZW12. Also, this work may be regarded as the extension of \citeTS,TS2 developed by T. Suslina concerned with the bounded Lipschitz domain.

Related

• Convergence Rates and Interior Estimates in Homogenization of Higher Order Elliptic Systems
• Precised approximations in elliptic homogenization beyond the periodic\n setting
• Boundary Estimates in Elliptic Homogenization
• Lipschitz regularity of homogenization with continuous coefficients: Dirichlet problem
• Combined Effects of Homogenization and Singular Perturbations: Quantitative Estimates