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

Autor:	Bakiev, S. M., Kon'kov, A. A.
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs 35J15 35J60 35J61 35J62 35J92
Druh dokumentu:	Working Paper
Popis:	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 $h \in W_{p, loc}^1 (M)$, $p > 1$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.13366 Zobrazit plný text záznamu View this record from Arxiv