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Mat. Zametki, 1998, Volume 64, Issue 6, Pages 830–838 (Mi mz1462)  

This article is cited in 10 scientific papers (total in 11 papers)

On a family of extremum problems and the properties of an integral

A. P. Buslaeva, V. A. Kondrat'evb, A. I. Nazarovc

a Moscow State Automobile and Road Technical University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
c Saint-Petersburg State University

Abstract: The following extremum problem is studied:
$$ \int _0^1(y"(t))^p dt/ \int _0^1(y'(t))^q dt \to\min $$
over all $y$, with $y(0)=y(1)=0$ and $y'(0)=y'(1)=0$, which leads to the integral
$$ \int_{\mathbb R}(\max(0,1+\mu x-|x|^q))^{1/p'} dx $$
and yields exact estimates for the eigenvalues of differential operators in the generalized Lagrange problem on the stability of a column.

DOI: https://doi.org/10.4213/mzm1462

Full text: PDF file (212 kB)
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English version:
Mathematical Notes, 1998, 64:6, 719–725

Bibliographic databases:

UDC: 517.972.8
Received: 19.12.1997

Citation: A. P. Buslaev, V. A. Kondrat'ev, A. I. Nazarov, “On a family of extremum problems and the properties of an integral”, Mat. Zametki, 64:6 (1998), 830–838; Math. Notes, 64:6 (1998), 719–725

Citation in format AMSBIB
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\by A.~P.~Buslaev, V.~A.~Kondrat'ev, A.~I.~Nazarov
\paper On a family of extremum problems and the properties of an integral
\jour Mat. Zametki
\yr 1998
\vol 64
\issue 6
\pages 830--838
\mathnet{http://mi.mathnet.ru/mz1462}
\crossref{https://doi.org/10.4213/mzm1462}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1691263}
\zmath{https://zbmath.org/?q=an:0944.49019}
\transl
\jour Math. Notes
\yr 1998
\vol 64
\issue 6
\pages 719--725
\crossref{https://doi.org/10.1007/BF02313029}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000080436700023}


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    Citing articles on Google Scholar: Russian citations, English citations
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    2. Croce, G, “On a generalized Wirtinger inequality”, Discrete and Continuous Dynamical Systems, 9:5 (2003), 1329  crossref  mathscinet  zmath  isi
    3. Lifshits, M, “Tail behavior of anisotropic norms for Gaussian random fields”, Comptes Rendus Mathematique, 336:1 (2003), 85  crossref  mathscinet  zmath  isi  scopus  scopus
    4. O. V. Besov, V. S. Vladimirov, V. V. Kozlov, S. M. Nikol'skii, Yu. S. Osipov, S. I. Pokhozhaev, V. A. Sadovnichii, “Vladimir Aleksandrovich Kondrat'ev (on his 70th birthday)”, Russian Math. Surveys, 61:6 (2006), 1189–1197  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Girao, P, “The shape of extrernal functions for Poincaré-Sobolev-type inequalities in a ball”, Journal of Functional Analysis, 237:1 (2006), 194  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Croce G., Henrot A., Pisante G., “An Isoperimetric Inequality for a Nonlinear Eigenvalue Problem”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 29:1 (2012), 21–34  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. E. V. Mukoseeva, A. I. Nazarov, “On symmetry of the extremal in some embedding theorems”, J. Math. Sci. (N. Y.), 210:6 (2015), 779–786  mathnet  crossref
    8. Brandolini B., Della Pietra F., Nitsch C., Trombetti C., “Symmetry Breaking in a Constrained Cheeger Type Isoperimetric Inequality”, ESAIM-Control OPtim. Calc. Var., 21:2 (2015), 359–371  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Kuznetsov N., Nazarov A., “Sharp Constants in the Poincaré, Steklov and Related Inequalities (a Survey)”, Mathematika, 61:2 (2015), 328–344  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Della Pietra F., Piscitelli G., “A saturation phenomenon for a nonlinear nonlocal eigenvalue problem”, NoDea-Nonlinear Differ. Equ. Appl., 23:6 (2016), 62  crossref  mathscinet  zmath  isi  scopus
    11. Ghisi M., Gobbino M., Rovellini G., “Symmetry-Breaking in a Generalized Wirtinger Inequality”, ESAIM-Control OPtim. Calc. Var., 24:4 (2018), 1381–1394  crossref  mathscinet  zmath  isi  scopus
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