Existence of Solutions to the Second Boundary-Value Problem for the $$p$$-Laplacian on Riemannian Manifolds
| Autor: | Andrej Alexandrovich Kon'kov, V. V. Brovkin |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Mathematical Notes. 109:171-183 |
| ISSN: | 1573-8876 0001-4346 |
| DOI: | 10.1134/s0001434621010211 |
| Popis: | 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 $$\partial M$$ . |
| Databáze: | OpenAIRE |
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