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arXiv · 1602.03610

Upper bounds on the first eigenvalue for the $p$-Laplacian

Guangyue Huang·Zhi Li
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Abstract

In this paper, we establish gradient estimates for positive solutions to the following equation with respect to the $p$-Laplacian $$\Delta_{p}u=-\lambda |u|^{p-2}u$$ with $p>1$ on a given complete Riemannian manifold. Consequently, we derive upper bound estimates of the first nontrivial eigenvalue of the $p$-Laplacian.

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Guangyue Huang, Zhi Li. 2016-02-11. Upper bounds on the first eigenvalue for the $p$-Laplacian. https://arxiv.org/abs/1602.03610

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