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Probl. Anal. Issues Anal., 2019, Volume 8(26), Issue 3, Pages 73–82 (Mi pa273)  

This article is cited in 1 scientific paper (total in 1 paper)

On solvability of the boundary value problems for harmonic function on noncompact Riemannian manifolds

A. G. Losev, E. A. Mazepa

Volgograd State University, 100 Universitetsky pr., Volgograd 400062, Russia

Abstract: We study questions of existence and belonging to the given functional class of solutions of the Laplace-Beltrami equations on a noncompact Riemannian manifold $M$ with no boundary. In the present work we suggest the concept of $\phi$-equivalency in the class of continuous functions and establish some interrelation between problems of existence of solutions of the Laplace-Beltrami equations on $M$ and off some compact $B \subset M$ with the same growth "at infinity". A new conception of $\phi$-equivalence classes of functions on $M$ develops and generalizes the concept of equivalence of function on $M$ and allows us to more accurately estimate the rate of convergence of the solution to boundary conditions.

Keywords: Riemannian manifold, harmonic function, boundary-value problems, $\phi$-equivalency.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation 2.852.2017/4.6
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (government task No. 2.852.2017/4.6).


DOI: https://doi.org/10.15393/j3.art.2019.7050

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Bibliographic databases:

UDC: 517.95
MSC: 31C12
Received: 14.08.2019
Revised: 30.09.2019
Accepted:23.09.2019
Language:

Citation: A. G. Losev, E. A. Mazepa, “On solvability of the boundary value problems for harmonic function on noncompact Riemannian manifolds”, Probl. Anal. Issues Anal., 8(26):3 (2019), 73–82

Citation in format AMSBIB
\Bibitem{LosMaz19}
\by A.~G.~Losev, E.~A.~Mazepa
\paper On solvability of the boundary value problems for harmonic function on noncompact Riemannian manifolds
\jour Probl. Anal. Issues Anal.
\yr 2019
\vol 8(26)
\issue 3
\pages 73--82
\mathnet{http://mi.mathnet.ru/pa273}
\crossref{https://doi.org/10.15393/j3.art.2019.7050}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000497499600007}
\elib{https://elibrary.ru/item.asp?id=41470781}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Brovkin, A. A. Kon'kov, “Existence of Solutions to the Second Boundary-Value Problem for the $p$-Laplacian on Riemannian Manifolds”, Math. Notes, 109:2 (2021), 171–183  mathnet  crossref  crossref  isi
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