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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 3, Pages 645–671 (Mi izv2156)  

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

Imbedding theorems and geometric inequalities

V. S. Klimov


Abstract: Imbedding theorems for Sobolev spaces with a symmetric norm are established. In particular, the results obtained lead to new imbedding theorems for Orlich–Sobolev spaces. The proof of the basic results is based on geometric inequalities of the type of the classical Brunn–Minkovskii inequality.
Bibliography: 30 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:3, 615–638

Bibliographic databases:

UDC: 513.881+517.5
MSC: Primary 46E30, 46E35; Secondary 52A40
Received: 27.02.1975

Citation: V. S. Klimov, “Imbedding theorems and geometric inequalities”, Izv. Akad. Nauk SSSR Ser. Mat., 40:3 (1976), 645–671; Math. USSR-Izv., 10:3 (1976), 615–638

Citation in format AMSBIB
\Bibitem{Kli76}
\by V.~S.~Klimov
\paper Imbedding theorems and geometric inequalities
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 3
\pages 645--671
\mathnet{http://mi.mathnet.ru/izv2156}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=420250}
\zmath{https://zbmath.org/?q=an:0332.46022}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 3
\pages 615--638
\crossref{https://doi.org/10.1070/IM1976v010n03ABEH001723}


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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. S. Klimov, “On imbedding theorems for anisotropic classes of functions”, Math. USSR-Sb., 55:1 (1986), 195–205  mathnet  crossref  mathscinet  zmath
    2. V. S. Klimov, “Functional inequalities and generalized capacities”, Sb. Math., 187:1 (1996), 39–52  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. S. Klimov, “On the symmetrization of anisotropic integral functionals”, Russian Math. (Iz. VUZ), 43:8 (1999), 23–29  mathnet  mathscinet  zmath  elib
    4. V. S. Klimov, E. S. Panasenko, “Functional Inequalities and Relative Capacities”, Math. Notes, 72:2 (2002), 193–203  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. S. Klimov, “Symmetrization of functions from Sobolev spaces”, Russian Math. (Iz. VUZ), 46:11 (2002), 41–47  mathnet  mathscinet  zmath  elib
    6. V. S. Klimov, “Izoperimetricheskie i funktsionalnye neravenstva”, Model. i analiz inform. sistem, 25:3 (2018), 331–342  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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