Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature

DOI10.1515/ADVGEOM.2007.009zbMath1121.58026MaRDI QIDQ5295335

Hui-Chun Zhang

Publication date: 27 July 2007

Published in: advg (Search for Journal in Brave)

zbMATH Keywords

Riemannian manifold\(p\)-Laplace operatorlower bound for the first eigenvalue

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Boundary value problems on manifolds (58J32)

Related Items (7)

The first eigenfunctions and eigenvalue of the \(p\)-Laplacian on Finsler manifolds ⋮ A remark on optimal weighted Poincaré inequalities for convex domains ⋮ Upper bounds on the first eigenvalue for the \(p\)-Laplacian ⋮ Sharp estimate on the first eigenvalue of the \(p\)-Laplacian ⋮ Sharp estimates on the first eigenvalue of the \(p\)-Laplacian with negative Ricci lower bound ⋮ Lower bound estimates for the first eigenvalue of the weighted \(p\)-Laplacian on smooth metric measure spaces ⋮ Regularity of stable solutions to quasilinear elliptic equations on Riemannian models

Cites Work

• A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
• Regularity for a more general class of quasilinear equations
• On the first eigenvalue of the \(p\)-Laplacian in a Riemannian manifold
• The first eigenvalue of the \(p\)-Laplacian on a compact Riemannian manifold.
• The \(\infty\)-eigenvalue problem
• First eigenvalue for the \(p\)-Laplace operator
• Eigenvalue problems for the \(p\)-Laplacian
• \(p\)-Laplace operator and diameter of manifolds
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0

This page was built for publication: Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature