Homogenization and boundary layers in domains of finite type

TL;DR

This paper establishes homogenization results for elliptic systems with periodic coefficients in finite type domains, providing explicit convergence rates that depend on the domain's dimension and type.

Contribution

It proves the homogenization theorem and derives an explicit algebraic convergence rate for elliptic systems in finite type domains with oscillating coefficients and boundary data.

Findings

Homogenization theorem for elliptic systems in finite type domains.

Explicit algebraic convergence rate depending on dimension and domain type.

Applicability to periodic, rapidly oscillating coefficients and boundary data.

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.