Quantitative Homogenization with Relatively Soft Inclusions and Interior Estimates

2018/05/10 by B. Chase Russell, Russell, B. Chase
Computer Science · Engineering · #35B27 #74B05 #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.1805.05183

openalex publication_date 2018/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish large-scale interior Lipschitz estimates for solutions to systems of linear elasticity with rapidly oscillating periodic coefficients and Dirichlet boundary conditions in domains with periodically placed inclusions of size O(ε) and magnitude δ by establishing H¹-convergence rates for such solutions. The interior estimates at the macroscopic scale are derived directly without the use of compactness via a Campanato-type scheme presented by S. Armstrong and C.K. Smart and that was adapted for uniformly elliptic equations in by Armstrong and Z. Shen.

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