Abstract
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 \(\partial M\).
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Funding
The research of the second author was supported by the Russian Science Foundation under grant 20-11-20272 and by RUDN (program 5-100).
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Brovkin, V.V., Kon’kov, A.A. Existence of Solutions to the Second Boundary-Value Problem for the \(p\)-Laplacian on Riemannian Manifolds. Math Notes 109, 171–183 (2021). https://doi.org/10.1134/S0001434621010211
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DOI: https://doi.org/10.1134/S0001434621010211