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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 4, Pages 718–733 (Mi izv1582)  

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

On $G$-compactness of a class of nondivergence elliptic operators of second order

V. V. Zhikov, M. M. Sirazhudinov


Abstract: This paper introduces the concept of $G$-convergence for nondivergence elliptic operators of second order. It is proved that the class of operators subject to the natural ellipticity inequalities and to a certain “cone” condition (Cordes' condition) is compact in the $G$-topology.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:1, 27–40

Bibliographic databases:

UDC: 517.9
MSC: 47F05
Received: 20.10.1980

Citation: V. V. Zhikov, M. M. Sirazhudinov, “On $G$-compactness of a class of nondivergence elliptic operators of second order”, Izv. Akad. Nauk SSSR Ser. Mat., 45:4 (1981), 718–733; Math. USSR-Izv., 19:1 (1982), 27–40

Citation in format AMSBIB
\Bibitem{ZhiSir81}
\by V.~V.~Zhikov, M.~M.~Sirazhudinov
\paper On $G$-compactness of a~class of nondivergence elliptic operators of second order
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 4
\pages 718--733
\mathnet{http://mi.mathnet.ru/izv1582}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=631435}
\zmath{https://zbmath.org/?q=an:0494.35033|0482.35039}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 1
\pages 27--40
\crossref{https://doi.org/10.1070/IM1982v019n01ABEH001409}


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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. V. L. Kamynin, “On passage to the limit in quasilinear elliptic equations with several independent variables”, Math. USSR-Sb., 60:1 (1988), 47–66  mathnet  crossref  mathscinet  zmath
    2. A. V. Pozhidaev, V. V. Yurinskii, “On the error of averaging symmetric elliptic systems”, Math. USSR-Izv., 35:1 (1990), 183–201  mathnet  crossref  mathscinet  zmath
    3. M. M. Sirazhudinov, “$G$-convergence and homogenization of generalized Beltrami operators”, Sb. Math., 199:5 (2008), 755–786  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. M. M. Sirazhudinov, S. P. Dzhamaludinova, “$G$-skhodimost i usrednenie odnogo klassa ellipticheskikh uravnenii vtorogo poryadka s kompleksnoznachnymi koeffitsientami”, Dagestanskie elektronnye matematicheskie izvestiya, 2014, no. 2, 87–100  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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