Geodesic
On~the Existence of Solutions of the Dirichlet Problem for the $p$-Laplacian on Riemannian Manifolds
Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 659-668

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We obtain a criterion for the existence of solutions of the problem $$ \Delta_p u=0 \quad\text{in}\quad M \setminus \partial M,\qquad u|_{\partial M}=h $$ with a bounded Dirichlet integral, where $M$ is an oriented complete Riemannian manifold with boundary and $h \in W_{p,\mathrm{loc}}^1 (M)$, $p > 1$.
Keywords: $p$-Laplacian, Dirichlet problem, Riemannian manifold. 
@article{MZM_2023_114_5_a1,
     author = {S. M. Bakiev and A. A. Kon'kov},
     title = {On~the {Existence} of {Solutions} of the {Dirichlet} {Problem} for the $p${-Laplacian} on {Riemannian} {Manifolds}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {659--668},
     publisher = {mathdoc},
     volume = {114},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a1/}
}
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S. M. Bakiev; A. A. Kon'kov. On~the Existence of Solutions of the Dirichlet Problem for the $p$-Laplacian on Riemannian Manifolds. Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 659-668. http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a1/