The first eigenvalue of the \(p\)-Laplacian on a compact Riemannian manifold.

DOI10.1016/S0362-546X(03)00209-8zbMath1043.53031OpenAlexW2021046950WikidataQ115339190 ScholiaQ115339190MaRDI QIDQ1413251

Shigeo Kawai, Nobumitsu Nakauchi

Publication date: 16 November 2003

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/s0362-546x(03)00209-8

zbMATH Keywords

Riemannian manifold\(p\)-Laplacianestimatenonlinear eigenvalue

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items

Comparison estimates on the first eigenvalue of a quasilinear elliptic system ⋮ Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature ⋮ First eigenvalue of the \(p\)-Laplace operator along the Ricci flow ⋮ The first eigenfunctions and eigenvalue of the \(p\)-Laplacian on Finsler manifolds ⋮ Lower bounds for the first eigenvalue of the \(p\)-Laplacian on compact manifolds with positive Ricci curvature ⋮ Lower bounds for the length of the second fundamental form via the first eigenvalue of the \(p\)-Laplacian ⋮ Sharp estimate on the first eigenvalue of the \(p\)-Laplacian ⋮ First eigenvalue monotonicity for the \(p\)-Laplace operator under the Ricci flow ⋮ First eigenvalue of the $p$-Laplacian on Kähler manifolds ⋮ Sharp spectral gap for the Finsler \(p\)-Laplacian ⋮ Sharp estimates on the first eigenvalue of the \(p\)-Laplacian with negative Ricci lower bound ⋮ Unnamed Item ⋮ Regularity of stable solutions to quasilinear elliptic equations on Riemannian models

Cites Work

• On nonlinear Rayleigh quotients
• A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
• On the first eigenvalue of the \(p\)-Laplacian in a Riemannian manifold
• The Fredholm alternative at the first eigenvalue for the one dimensional \(p\)-Laplacian
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The first eigenvalue of the \(p\)-Laplacian on a compact Riemannian manifold.