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Funktsional. Anal. i Prilozhen., 2017, Volume 51, Issue 2, Pages 92–96 (Mi faa3457)  

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

On homogenization for non-self-adjoint locally periodic elliptic operators

N. N. Senik

St. Petersburg State University, St. Petersburg, Russia

Abstract: In this note we consider the homogenization problem for a matrix locally periodic elliptic operator on $R^d$ of the form $\mathcal A^\varepsilon=-\operatorname{div}A(x,x/\varepsilon)\nabla$. The function $A$ is assumed to be Hölder continuous with exponent $s\in[0,1]$ in the “slow” variable and bounded in the “fast” variable. We construct approximations for $(A^\varepsilon-\mu)^{-1}$, including one with a corrector, and for $(-\Delta)^{s/2}(A^\varepsilon-\mu)^{-1}$ in the operator norm on $L_2(R^d)^n$. For $s\ne0$, we also give estimates of the rates of approximation.

Keywords: homogenization, operator error estimates, locally periodic operators, effective operator, corrector.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00087
Contest «Young Russian Mathematics»
Research supported by Young Russian Mathematics award and RFBR grant 16-01-00087.


DOI: https://doi.org/10.4213/faa3457

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English version:
Functional Analysis and Its Applications, 2017, 51:2, 152–156

Bibliographic databases:

Document Type: Article
UDC: 517.956.2
Received: 23.01.2017

Citation: N. N. Senik, “On homogenization for non-self-adjoint locally periodic elliptic operators”, Funktsional. Anal. i Prilozhen., 51:2 (2017), 92–96; Funct. Anal. Appl., 51:2 (2017), 152–156

Citation in format AMSBIB
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  • https://doi.org/10.4213/faa3457
  • http://mi.mathnet.ru/eng/faa/v51/i2/p92

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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. Senik N.N., “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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