Quantitative Estimates on Periodic Homogenization of Nonlinear Elliptic Operators

2018/07/28 by Li Wang, Qiang Xu, Wang, Li +3
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.1807.10865

openalex publication_date 2018/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we are interested in the periodic homogenization of quasilinear elliptic equations. We obtain error estimates O(ε^1/2) for a C^1,1 domain, and O(ε^σ) for a Lipschitz domain, in which σ∈(0,1/2) is close to zero. Based upon the convergence rates, an interior Lipschitz estimate, as well as a boundary Hölder estimate can be developed at large scales without any smoothness assumption, and these will implies reverse Hölder estimates established for a C¹ domain. By a real method developed by Z.Shen \citeS3, we consequently derive a global W^1,p estimate for 2≤ p

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