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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 1, Pages 3–21 (Mi izv1468)  

This article is cited in 6 scientific papers (total in 6 papers)

On the question of extension of multidimensional variational problems

F. V. Guseinov


Abstract: The extension of multidimensional variational problems is investigated. In particular, a multidimensional analogue of the Bogolyubov theorem on extension of a simple problem of the calculus of variations is proved. The problem of the closure of the class of functions of several variables with derivatives in a given set is considered. This problem is closely connected with the extension of variational problems.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:1, 1–19

Bibliographic databases:

UDC: 517.97
MSC: Primary 49A29, 49B99; Secondary 46E35
Received: 25.03.1983

Citation: F. V. Guseinov, “On the question of extension of multidimensional variational problems”, Izv. Akad. Nauk SSSR Ser. Mat., 50:1 (1986), 3–21; Math. USSR-Izv., 28:1 (1987), 1–19

Citation in format AMSBIB
\Bibitem{Gus86}
\by F.~V.~Guseinov
\paper On the question of extension of multidimensional variational problems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 1
\pages 3--21
\mathnet{http://mi.mathnet.ru/izv1468}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=835563}
\zmath{https://zbmath.org/?q=an:0613.49009|0597.49006}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 1
\pages 1--19
\crossref{https://doi.org/10.1070/IM1987v028n01ABEH000863}


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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. Sychev M., “Characterization of Homogeneous Scalar Variational Problems Solvable for All Boundary Data”, Proc. R. Soc. Edinb. Sect. A-Math., 130:Part 3 (2000), 611–631  mathscinet  zmath  isi
    2. Sychev M., “Comparing Two Methods of Resolving Homogeneous Differential Inclusions”, Calc. Var. Partial Differ. Equ., 13:2 (2001), 213–229  crossref  mathscinet  zmath  isi
    3. Muller S., Sychev M., “Optimal Existence Theorems for Nonhomogeneous Differential Inclusions”, J. Funct. Anal., 181:2 (2001), 447–475  crossref  mathscinet  isi
    4. Sychev M., “Attainment and Relaxation Results in Special Classes of Deformations”, Calc. Var. Partial Differ. Equ., 19:2 (2004), 183–210  crossref  mathscinet  zmath  isi
    5. M. A. Sychev, “Theorems on lower semicontinuity and relaxation for integrands with fast growth”, Siberian Math. J., 46:3 (2005), 540–554  mathnet  crossref  mathscinet  zmath  isi  elib
    6. Farhad Hüsseinov, “Relaxation and nonoccurrence of the Lavrentiev phenomenon for nonconvex problems”, Acta. Math. Sin.-English Ser, 2013  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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