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Algebra i Analiz, 2010, Volume 22, Issue 5, Pages 69–103 (Mi aa1205)  

This article is cited in 19 scientific papers (total in 19 papers)

Research Papers

Homogenization of periodic differential operators of high order

N. A. Veniaminov

St. Petersburg State University, Faculty of Physics, St. Petersburg, Russia
References:
Abstract: A periodic differential operator of the form $A_\varepsilon=(\mathbf D^p)^*g(\mathbf x/\varepsilon)\mathbf D^p$ is considered on $L_2(\mathbb R^d)$; here $g(x)$ is a positive definite symmetric tensor of order $2p$ periodic with respect to a lattice $\Gamma$. The behavior of the resolvent of the operator $A_\varepsilon$ as $\varepsilon\to0$ is studied. It is shown that the resolvent $(A_\varepsilon+I)^{-1}$ converges in the operator norm to the resolvent of the effective operator $A^0$ with constant coefficients. For the norm of the difference of resolvents, an estimate of order $\varepsilon$ is obtained.
Keywords: periodic differential operators, averaging, homogenization, threshold effect, operators of high order.
Received: 28.01.2010
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 5, Pages 751–775
DOI: https://doi.org/10.1090/S1061-0022-2011-01166-5
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: N. A. Veniaminov, “Homogenization of periodic differential operators of high order”, Algebra i Analiz, 22:5 (2010), 69–103; St. Petersburg Math. J., 22:5 (2011), 751–775
Citation in format AMSBIB
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\paper Homogenization of periodic differential operators of high order
\jour Algebra i Analiz
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\pages 751--775
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  • https://www.mathnet.ru/eng/aa1205
  • https://www.mathnet.ru/eng/aa/v22/i5/p69
  • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
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    References:80
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