Geodesic
On solvability of the boundary value problems for harmonic function on noncompact Riemannian manifolds
Problemy analiza, Tome 8 (2019) no. 3, pp. 73-82

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     author = {A. G. Losev and E. A. Mazepa},
     title = {On solvability of the boundary value problems for  harmonic function on noncompact {Riemannian} manifolds},
     journal = {Problemy analiza},
     pages = {73--82},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_3_a6/}
}
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A. G. Losev; E. A. Mazepa. On solvability of the boundary value problems for  harmonic function on noncompact Riemannian manifolds. Problemy analiza, Tome 8 (2019) no. 3, pp. 73-82. http://geodesic.mathdoc.fr/item/PA_2019_8_3_a6/