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Mat. Tr., 2013, Volume 16, Number 2, Pages 69–88 (Mi mt260)  

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

On the mean value property for polyharmonic functions in the ball

V. V. Karachik

South Ural State University, Chelyabinsk, Russia

Abstract: We obtain the mean value property for the normal derivatives of a polyharmonic function with respect to the unit sphere. We find the values of a polyharmonic function and its Laplacians at the center of the unit ball expressed via the integrals of the normal derivatives of this function over the unit sphere.

Key words: polyharmonic function, mean value property, normal derivatives on the sphere.

Full text: PDF file (223 kB)
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English version:
Siberian Advances in Mathematics, 2014, 24:3, 169–182

Bibliographic databases:

UDC: 517.575
Received: 15.04.2013

Citation: V. V. Karachik, “On the mean value property for polyharmonic functions in the ball”, Mat. Tr., 16:2 (2013), 69–88; Siberian Adv. Math., 24:3 (2014), 169–182

Citation in format AMSBIB
\Bibitem{Kar13}
\by V.~V.~Karachik
\paper On the mean value property for polyharmonic functions in the ball
\jour Mat. Tr.
\yr 2013
\vol 16
\issue 2
\pages 69--88
\mathnet{http://mi.mathnet.ru/mt260}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184038}
\transl
\jour Siberian Adv. Math.
\yr 2014
\vol 24
\issue 3
\pages 169--182
\crossref{https://doi.org/10.3103/S1055134414030031}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. V. V. Karachik, “Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball”, Comput. Math. Math. Phys., 54:7 (2014), 1122–1143  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. I. A. Gulyaschikh, “Zadacha Neimana dlya poligarmonicheskogo uravneniya v edinichnom share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:2 (2015), 70–72  mathnet  elib
    3. V. V. Karachik, “Solution of the Dirichlet problem with polynomial data for the polyharmonic equation in a ball”, Differ. Equ., 51:8 (2015), 1033–1042  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Adv. Math., 27:2 (2017), 103–118  mathnet  crossref  crossref  elib
    5. V. V. Karachik, B. T. Torebek, “On one mathematical model described by boundary value problem for the biharmonic equation”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:4 (2016), 40–52  mathnet  crossref  elib
    6. B. Turmetov, “On some boundary value problems for nonhomogenous polyharmonic equation with boundary operators of fractional order”, Acta Math. Sci., 36:3 (2016), 831–846  crossref  mathscinet  zmath  isi  scopus
    7. B. Kh. Turmetov, V. V. Karachik, “About one boundary value problem for the biharmonic equation”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conf. Proc., 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2016, UNSP 040015  crossref  isi  scopus
    8. V. V. Karachik, “Integralnye tozhdestva na sfere dlya normalnykh proizvodnykh poligarmonicheskikh funktsii”, Sib. elektron. matem. izv., 14 (2017), 533–551  mathnet  crossref  mathscinet  zmath
    9. V. V. Karachik, “Generalized third boundary value problem for the biharmonic equation”, Differ. Equ., 53:6 (2017), 756–765  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    10. V. V. Karachik, “Solving a problem of Robin type for biharmonic equation”, Russian Math. (Iz. VUZ), 62:2 (2018), 34–48  mathnet  crossref  isi
  • Математические труды Siberian Advances in Mathematics
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