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Algebra i Analiz, 2008, Volume 20, Issue 2, Pages 19–42 (Mi aa504)  
This article is cited in 26 scientific papers (total in 26 papers)

Research Papers

Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients

D. I. Borisovab

a Bashkir State Pedagogical University
b Nuclear Physics Institute, Academy of Sciences of the Czech Republic
Full-text PDF (330 kB) Citations (26)
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Abstract: A singularly perturbed second order elliptic system in the entire space is treated. The coefficients of the systems oscillate rapidly and depend both on the slow and fast variables. The homogenized operator is obtained and, in the uniform norm sense, the leading terms of the asymptotic expansion are constructed for the resolvent of the operator described by the system. The convergence of the spectrum is established, and examples are given.
Keywords: Homogenization of differentiable operators, unbounded domain, fast and slow variables.
Received: 30.11.2006
English version:
St. Petersburg Mathematical Journal, 2009, Volume 20, Issue 2, Pages 175–191
DOI: https://doi.org/10.1090/S1061-0022-09-01043-7
Bibliographic databases:
Document Type: Article
MSC: 35B27
Language: Russian
Citation: D. I. Borisov, “Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients”, Algebra i Analiz, 20:2 (2008), 19–42; St. Petersburg Math. J., 20:2 (2009), 175–191
Citation in format AMSBIB
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\by D.~I.~Borisov
\paper Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients
\jour Algebra i Analiz
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\vol 20
\issue 2
\pages 19--42
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\transl
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 2
\pages 175--191
\crossref{https://doi.org/10.1090/S1061-0022-09-01043-7}
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    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:690
    Full-text PDF :246
    References:79
    First page:11
     
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