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This article is cited in 5 scientific papers (total in 5 papers)
On solvability of the boundary value problems for the inhomogeneous elliptic equations 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 a given functional class of solutions of the inhomogeneous elliptic equations
$\Delta u-c(x)u=g(x)$, where $c(x)\geq 0$, $g(x)$ are Hölder fuctions on a noncompact Riemannian manifold $M$ without boundary.
In this work we develop an approach to evaluation of solutions to boundary-value problems for linear and quasilinear equations of
the elliptic type on arbitrary noncompact Riemannian manifolds. Our technique is essentially based on an approach from the papers by
E. A. Mazepa and S. A. Korol'kov connected with an introduction of equivalency classes of functions
and representations. We investigate the relationship between the existence of solutions of this equation on $M$ and outside some compact set $B\subset M$ with the same growth "at infinity".
Keywords:
Riemannian manifold, nonhomogeneous elliptic equations, boundary-value problems.
Received: 29.05.2018 Revised: 28.08.2018 Accepted: 31.08.2018
Citation:
A. G. Losev, E. A. Mazepa, “On solvability of the boundary value problems for the inhomogeneous elliptic equations on noncompact Riemannian manifolds”, Probl. Anal. Issues Anal., 7(25), special issue (2018), 101–112
Linking options:
https://www.mathnet.ru/eng/pa235 https://www.mathnet.ru/eng/pa/v25/i3/p101
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