On Homogenization of Locally Periodic Elliptic and Parabolic Operators

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let Ω be a C1,s bounded domain (s > 1/2) in ℝd, and let Aε= − div A(x, x/ ε) ∇ be a matrix elliptic operator on Ω with Dirichlet boundary condition. We suppose that ε is small and the function A is Lipschitz in the first variable and periodic in the second one, so the coefficients of Aε are locally periodic. For μ in the resolvent set, we are interested in finding the rates of approximations, as ε → 0, for (Aε−μρε)−1 and ∇(Aε−μρε)−1 in the operator topology on L2. Here ρε(x)= ρ(x,x/ε) is a positive definite locally periodic function with ρ satisfying the same assumptions as A. Keeping track of the rate dependence on both ε and μ, we then proceed to similar questions for the solution to the initial boundary-value problem ρεtvε= − Aεvε.

Original languageEnglish
Pages (from-to)68-72
Number of pages5
JournalFunctional Analysis and its Applications
Volume54
Issue number1
DOIs
StatePublished - 1 Jan 2020

Scopus subject areas

  • Analysis
  • Applied Mathematics

Keywords

  • elliptic systems
  • homogenization
  • locally periodic operators
  • operator error estimates
  • parabolic systems

Fingerprint

Dive into the research topics of 'On Homogenization of Locally Periodic Elliptic and Parabolic Operators'. Together they form a unique fingerprint.

Cite this