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Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 1, Pages 85–89 (Mi faa3226)  

This article is cited in 2 scientific papers (total in 2 papers)

Brief communications

On Homogenization for Non-Self-Adjoint Periodic Elliptic Operators on an Infinite Cylinder

N. N. Senik

Saint Petersburg State University

Abstract: We consider an operator $\mathcal{A}^{\varepsilon}$ on $L_{2}(\mathbb{R}^{d_{1}}\times\mathbb{T}^{d_{2}})$ ($d_{1}$ is positive, while $d_{2}$ can be zero) given by $\mathcal{A}^{\varepsilon}=-\operatorname{div} A(\varepsilon^{-1}x_{1},x_{2})\nabla$, where $A$ is periodic in the first variable and smooth in a sense in the second. We present approximations for $(\mathcal{A}^{\varepsilon}-\mu)^{-1}$ and $\nabla(\mathcal{A}^{\varepsilon}-\mu)^{-1}$ (with appropriate $\mu$) in the operator norm when $\varepsilon$ is small. We also provide estimates for the rates of approximation that are sharp with respect to the order.

Keywords: homogenization, operator error estimates, periodic differential operators, effective operator, corrector

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00760
Saint Petersburg State University 0.38.237.2014


DOI: https://doi.org/10.4213/faa3226

Full text: PDF file (115 kB)
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English version:
Functional Analysis and Its Applications, 2016, 50:1, 71–75

Bibliographic databases:

UDC: 517.956.2
Received: 13.10.2015

Citation: N. N. Senik, “On Homogenization for Non-Self-Adjoint Periodic Elliptic Operators on an Infinite Cylinder”, Funktsional. Anal. i Prilozhen., 50:1 (2016), 85–89; Funct. Anal. Appl., 50:1 (2016), 71–75

Citation in format AMSBIB
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\paper On Homogenization for Non-Self-Adjoint Periodic Elliptic Operators on an Infinite Cylinder
\jour Funktsional. Anal. i Prilozhen.
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\pages 85--89
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  • https://doi.org/10.4213/faa3226
  • http://mi.mathnet.ru/eng/faa/v50/i1/p85

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. N. Senik, “On homogenization for non-self-adjoint locally periodic elliptic operators”, Funct. Anal. Appl., 51:2 (2017), 152–156  mathnet  crossref  crossref  isi  elib
    2. N. N. Senik, “Homogenization for non-self-adjoint periodic elliptic operators on an infinite cylinder”, SIAM J. Math. Anal., 49:2 (2017), 874–898  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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