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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 318, Pages 60–74 (Mi znsl662)  
This article is cited in 44 scientific papers (total in 44 papers)

Homogenization of a multidimensional periodic elliptic operator in a neighbourhood of the edge of the internal gap

M. Sh. Birman, T. A. Suslina

Saint-Petersburg State University
Full-text PDF (226 kB) Citations (44)
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Abstract: The homogenization procedure for a multidimensional periodic Schrödinger operator near the edge of an internal gap is discussed. Approximation for the resolvent in the small period limit, with respect to the operator norm in $L_2(\mathbb{R}^d)$, is obtained. This approximation contains oscillations, but in a simpler form than the resolvent of the initial operator.
Received: 12.03.2004
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 136, Issue 2, Pages 3682–3690
DOI: https://doi.org/10.1007/s10958-006-0192-9
Bibliographic databases:
UDC: 517.956
Language: Russian
Citation: M. Sh. Birman, T. A. Suslina, “Homogenization of a multidimensional periodic elliptic operator in a neighbourhood of the edge of the internal gap”, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Zap. Nauchn. Sem. POMI, 318, POMI, St. Petersburg, 2004, 60–74; J. Math. Sci. (N. Y.), 136:2 (2006), 3682–3690
Citation in format AMSBIB
\Bibitem{BirSus04}
\by M.~Sh.~Birman, T.~A.~Suslina
\paper Homogenization of a~multidimensional periodic elliptic operator in a~neighbourhood of the edge of the internal gap
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~36
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 318
\pages 60--74
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl662}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2120232}
\zmath{https://zbmath.org/?q=an:1108.35008}
\elib{https://elibrary.ru/item.asp?id=9129102}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 136
\issue 2
\pages 3682--3690
\crossref{https://doi.org/10.1007/s10958-006-0192-9}
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    • This publication is cited in the following 44 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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