Geodesic
Existence of Solutions to the Second Boundary-Value Problem for the $p$-Laplacian on Riemannian Manifolds
Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 180-195.

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We obtain necessary and sufficient conditions for the existence of solutions to the boundary-value problem $$ \Delta_p u=f\quad\text{on}\quad M,\qquad |\nabla u|^{p-2}\,\frac {\partial u}{\partial \nu}\bigg|_{\partial M}=h, $$ 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. 
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     title = {Existence of {Solutions} to the {Second} {Boundary-Value} {Problem} for the $p${-Laplacian} on {Riemannian} {Manifolds}},
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V. V. Brovkin; A. A. Kon'kov. Existence of Solutions to the Second Boundary-Value Problem for the $p$-Laplacian on Riemannian Manifolds. Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 180-195. http://geodesic.mathdoc.fr/item/MZM_2021_109_2_a2/

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