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J. Sib. Fed. Univ. Math. Phys., 2009, Volume 2, Issue 2, Pages 146–157 (Mi jsfu60)  

This article is cited in 9 scientific papers (total in 9 papers)

On Inequalities of the Friedrichs type for Combined Domains

Viktor K. Andreev

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

Abstract: Integral inequalities of the Friedrichs type for combined domains with plane and cylindrical symmetries are proved. The optimal constants in the right-hand sides of the inequalities are found. These constants depend on physical and geometrical parameters of the domains. Some generalizations of these inequalities to domains of a different shape are considered.

Keywords: a priori estimate, Friedrichs inequality, variational problem.

Full text: PDF file (237 kB)
References: PDF file   HTML file
UDC: 517.994
Received: 18.02.2009
Received in revised form: 20.03.2009
Accepted: 10.04.2009

Citation: Viktor K. Andreev, “On Inequalities of the Friedrichs type for Combined Domains”, J. Sib. Fed. Univ. Math. Phys., 2:2 (2009), 146–157

Citation in format AMSBIB
\Bibitem{And09}
\by Viktor~K.~Andreev
\paper On Inequalities of the Friedrichs type for Combined Domains
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2009
\vol 2
\issue 2
\pages 146--157
\mathnet{http://mi.mathnet.ru/jsfu60}


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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. Viktor K. Andreev, Alexander P. Chupakhin, “The motion of a binary mixture and viscous liquid in a circular pipe under the action of an unsteady pressure gradient”, Zhurn. SFU. Ser. Matem. i fiz., 3:2 (2010), 135–145  mathnet
    2. Viktor K. Andreev, Vladimir V. Kuznetsov, “Termokapillyarnoe dvizhenie dvukh vyazkikh zhidkostei v tsilindricheskoi trube”, Zhurn. SFU. Ser. Matem. i fiz., 3:4 (2010), 461–474  mathnet
    3. Andreev V.K., “Properties of the solution of the adjoint problem describing the motion of viscous fluids in a tube”, Differ. Equ., 47:5 (2011), 671–680  crossref  mathscinet  zmath  isi  elib  scopus
    4. Victor K. Andreev, “Unsteady 2D motions a viscous fluid described by partially invariant solutions to the Navier–Stokes equations”, Zhurn. SFU. Ser. Matem. i fiz., 8:2 (2015), 140–147  mathnet
    5. V. K. Andreev, M. V. Efimova, “Properties of solutions for the problem of a joint slow motion of a liquid and a binary mixture in a two-dimensional channel”, J. Appl. Industr. Math., 12:3 (2018), 395–408  mathnet  crossref  crossref  elib
    6. Victor K. Andreev, Marina V. Efimova, “A priori estimates of the adjoint problem describing the slow flow of a binary mixture and a fluid in a channel”, Zhurn. SFU. Ser. Matem. i fiz., 11:4 (2018), 482–493  mathnet  crossref
    7. Evgeniy P. Magdenko, “The influence of changes in the internal energy of the interface on a two-layer flow in a cylinder”, Zhurn. SFU. Ser. Matem. i fiz., 12:2 (2019), 213–221  mathnet  crossref
    8. Victor K. Andreev, Evgeniy P. Magdenko, “A priori estimates of the conjugate problem describing an axisymmetric thermocapillary motion for small Marangoni number”, Zhurn. SFU. Ser. Matem. i fiz., 12:4 (2019), 483–495  mathnet  crossref
    9. O. L. Boziev, “O slabykh resheniyakh nagruzhennogo giperbolicheskogo uravneniya s odnorodnymi kraevymi usloviyami”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 11:2 (2019), 5–13  mathnet  crossref  elib
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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