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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
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.
Received: 14.08.2019 Revised: 30.09.2019 Accepted: 23.09.2019
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
Linking options:
https://www.mathnet.ru/eng/pa273 https://www.mathnet.ru/eng/pa/v26/i3/p73
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Abstract page: | 195 | Full-text PDF : | 64 | References: | 22 |
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