Upper bounds on the first eigenvalue for the p-Laplacian

2016/02/11 by Guangyue Huang, Zhi Li, Huang, Guangyue +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1602.03610

Abstract

In this paper, we establish gradient estimates for positive solutions to the following equation with respect to the p-Laplacian Δ_pu=-λ|u|^p-2u 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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