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Sbornik: Mathematics, 2016, Volume 207, Issue 3, Pages 418–443
DOI: https://doi.org/10.1070/SM8486
(Mi sm8486)
 

This article is cited in 4 scientific papers (total in 4 papers)

The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization

S. E. Pastukhova

Moscow Technological University
References:
Abstract: We prove an $L^2$-estimate for the homogenization of an elliptic operator $A_\varepsilon$ in a domain $\Omega$ with a Neumann boundary condition on the boundary $\partial\Omega$. The coefficients of the operator $A_\varepsilon$ are rapidly oscillating over different groups of variables with periods of different orders of smallness as $\varepsilon\to 0$. We assume minimal regularity of the data, which makes it possible to impart to the result the meaning of an estimate in the operator $(L^2(\Omega)\to L^2(\Omega))$-norm for the difference of the resolvents of the original and homogenized problems. We also find an approximation to the resolvent of the original problem in the operator $(L^2(\Omega)\to H^1(\Omega))$-norm.
Bibliography: 24 titles.
Keywords: multiscale homogenization, operator estimates for homogenization, Steklov smoothing.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00192
Russian Science Foundation 14-11-00398
This research was supported by the Russian Foundation for Basic Research (grant no. 14-01-00192) and the Russian Science Foundation (project no. 14-11-00398).
Received: 04.02.2015 and 24.05.2015
Bibliographic databases:
Document Type: Article
UDC: 517.956.8
MSC: Primary 35B27; Secondary 35J57
Language: English
Original paper language: Russian
Citation: S. E. Pastukhova, “The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization”, Sb. Math., 207:3 (2016), 418–443
Citation in format AMSBIB
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\by S.~E.~Pastukhova
\paper The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization
\jour Sb. Math.
\yr 2016
\vol 207
\issue 3
\pages 418--443
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\crossref{https://doi.org/10.1070/SM8486}
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  • https://www.mathnet.ru/eng/sm/v207/i3/p111
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:539
    Russian version PDF:161
    English version PDF:24
    References:89
    First page:47
     
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