Homogenization and boundary layers in domains of finite type

2016/12/16 by Jinping Zhuge, Zhuge, Jinping
Computer Science · Engineering · #35B27 #35J57 #74Q05 #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.1612.05383

openalex publication_date 2016/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the homogenization of Dirichlet problem of elliptic systems in a bounded, smooth domain of finite type. Both the coefficients of the elliptic operator and the Dirichlet boundary data are assumed to be periodic and rapidly oscillating. We prove the theorem of homogenization and obtain an algebraic rate of convergence that depends explicitly on dimension and the type of the domain.

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