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Mat. Zametki, 2021, Volume 109, Issue 2, Pages 180–195 (Mi mz12785)  

Existence of Solutions to the Second Boundary-Value Problem for the $p$-Laplacian on Riemannian Manifolds

V. V. Brovkin, A. A. Kon'kov

Lomonosov Moscow State University

Abstract: We obtain necessary and sufficient conditions for the existence of solutions to the boundary-value problem
$$ \Delta_p u=f\quadon\quad M,\qquad |\nabla u|^{p-2} \frac {\partial u}{\partial \nu}|_{\partial M}=h, $$
where $p > 1$ is a real number, $M$ is a connected oriented complete Riemannian manifold with boundary, and $\nu$ is the outer normal vector to $\partial M$.

Keywords: $p$-Laplacian, Riemannian manifold, Dirichlet integral.

Funding Agency Grant Number
Russian Science Foundation 20-11-20272
Ministry of Education and Science of the Russian Federation 5-100
The research of the second author was supported by the Russian Science Foundation under grant 20-11-20272 and by RUDN (program 5-100).


DOI: https://doi.org/10.4213/mzm12785

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English version:
Mathematical Notes, 2021, 109:2, 171–183

Bibliographic databases:

UDC: 517.954
Received: 08.05.2020
Revised: 14.07.2020

Citation: V. V. Brovkin, A. A. Kon'kov, “Existence of Solutions to the Second Boundary-Value Problem for the $p$-Laplacian on Riemannian Manifolds”, Mat. Zametki, 109:2 (2021), 180–195; Math. Notes, 109:2 (2021), 171–183

Citation in format AMSBIB
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\by V.~V.~Brovkin, A.~A.~Kon'kov
\paper Existence of Solutions to the Second Boundary-Value Problem for the $p$-Laplacian on Riemannian Manifolds
\jour Mat. Zametki
\yr 2021
\vol 109
\issue 2
\pages 180--195
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\crossref{https://doi.org/10.4213/mzm12785}
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