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Problemy Analiza — Issues of Analysis, 2019, Volume 8(26), Issue 3, Pages 73–82
DOI: https://doi.org/10.15393/j3.art.2019.7050
(Mi pa273)
 

This article is cited in 7 scientific papers (total in 7 papers)

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
Full-text PDF (364 kB) Citations (7)
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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).
Received: 14.08.2019
Revised: 30.09.2019
Accepted: 23.09.2019
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 31C12
Language: English
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
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\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
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\crossref{https://doi.org/10.15393/j3.art.2019.7050}
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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