Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary

DOI10.1515/form.2011.115zbMath1327.35275arXiv1002.0620OpenAlexW2963103014MaRDI QIDQ4915084

Bin Xu, Yiqian Shi

Publication date: 16 April 2013

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.0620

zbMATH Keywords

gradient estimatecompact manifoldDirichlet eigenfunction

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (1)

The gradient estimate of a Neumann eigenfunction on a compact manifold with boundary

Cites Work

• Eigenfunction and Bochner Riesz estimates on manifolds with boundary
• Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions
• Metric properties of eigenfunctions of the Laplace operator on manifolds
• On the boundedness of functions of (pseudo-) differential operators on compact manifolds
• Nodal sets of eigenfunctions on Riemannian manifolds
• Derivatives of the spectral function and Sobolev norms of eigenfunctions on a closed Riemannian manifold
• Gradient estimate of an eigenfunction on a compact Riemannian manifold without boundary
• UNIFORM BOUNDS FOR EIGENFUNCTIONS OF THE LAPLACIAN ON MANIFOLDS WITH BOUNDARY*
• Local Asymmetry and the Inner Radius of Nodal Domains
• Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem

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