Asymptotics for the principal eigenvalue of the \(p\)-Laplacian on the ball as \(p\) approaches 1

DOI10.1016/J.NA.2013.07.026zbMath1281.35064OpenAlexW1994550493MaRDI QIDQ2637684

Pavel Drábek, Jiří Benedikt

Publication date: 13 February 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2013.07.026

zbMATH Keywords

asymptotic analysisspecial functionsPoincaré constanteigenvalue problem for \(p\)-Laplacianestimates of principal eigenvalue

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Gamma, beta and polygamma functions (33B15) Variational methods for eigenvalues of operators (49R05) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (8)

On a p-Laplacian eigenvalue problem with supercritical exponent ⋮ Monotonicity properties for the variational Dirichlet eigenvalues of the \(p\)-Laplace operator ⋮ Asymptotic behavior and monotonicity of radial eigenvalues for the \(p\)-Laplacian ⋮ Computing the first eigenpair of the \(p\)-Laplacian in annuli ⋮ Lower Bounds for the Principal Eigenvalue of the p-Laplacian on the Unit Ball ⋮ Existence of radially symmetric solutions of the inhomogeneous \(p\)-Laplace equation ⋮ Computing the best constant in the Sobolev inequality for a ball ⋮ Gelfand-type problems involving the 1-Laplacian operator

Cites Work

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• Estimates of the principal eigenvalue of the \(p\)-Laplacian
• Solutions of the Cheeger problem via torsion functions
• Computing the first eigenvalue of the \(p\)-Laplacian via the inverse power method
• Computing the first eigenpair of the \(p\)-Laplacian via inverse iteration of sublinear supersolutions
• A Picone's identity for the p-Laplacian and applications
• Positive Solutions for the p-Laplacian and Bounds for its First Eigenvalue

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