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arXiv · 2302.13366

On the existence of solutions of the Dirichlet problem for $p$-Laplacian on Riemannian manifolds

S. M. Bakiev·A. A. Kon'kov
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Abstract

We obtain a criterion for the existence of solutions of the problem $$ \Delta_p u = 0 \quad \mbox{in } M \setminus \partial M, \quad \left. u \right|_{ \partial M } = h, $$ with the bounded Dirichlet integral, where $M$ is an oriented complete Riemannian manifold with boundary and $h \in W_{p, loc}^1 (M)$, $p > 1$.

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S. M. Bakiev, A. A. Kon'kov. 2023-02-26. On the existence of solutions of the Dirichlet problem for $p$-Laplacian on Riemannian manifolds. https://arxiv.org/abs/2302.13366

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