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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2017, Volume 14, Pages 533–551
DOI: https://doi.org/10.17377/semi.2017.14.046 (Mi semr804) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Real, complex and functional analysis

Integral identities on a sphere for normal derivatives of polyharmonic functions

V. V. Karachik

South Ural State University, pr. Lenina, 76, 454080, Chelyabinsk, Russia
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DOI: https://doi.org/10.17377/semi.2017.14.046
Abstract: Identities for the integrals over the unit sphere of the products of linear combinations of normal derivatives of polyharmonic function in the unit ball and homogeneous harmonic polynomials are obtained. Basing on these identities the necessary conditions for the values on the unit sphere of polynomials on normal derivatives of polyharmonic functions are derived. Illustrative examples are given.
Keywords: polyharmonic functions, higher order normal derivatives, integral identities on the sphere.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011.
Received December 16, 2016, published June 2, 2017
Bibliographic databases:
Document Type: Article
UDC: 517.575
MSC: 35B30
Language: Russian
Citation: V. V. Karachik, “Integral identities on a sphere for normal derivatives of polyharmonic functions”, Sib. Èlektron. Mat. Izv., 14 (2017), 533–551
Citation in format AMSBIB
\Bibitem{Kar17}
\by V.~V.~Karachik
\paper Integral identities on a sphere for normal derivatives of polyharmonic functions
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 533--551
\mathnet{http://mi.mathnet.ru/semr804}
\crossref{https://doi.org/10.17377/semi.2017.14.046}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3663288}
\zmath{https://zbmath.org/?q=an:1383.31001}
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