Eigenfunction estimates for Neumann Laplacian and applications to multiplier problems

DOI10.1090/S0002-9939-2011-10782-2zbMath1226.35059OpenAlexW1974034906MaRDI QIDQ3093444

Xiangjin Xu

Publication date: 17 October 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-10782-2

zbMATH Keywords

gradient estimate\(L^{\infty}\) estimatespectral clusterNeumann LaplacianHörmander multiplier theoremBochner Riesz means

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary value problems on manifolds (58J32)

Related Items (4)

Boundedness of spectral multipliers of generalized Laplacians on compact manifolds with boundary ⋮ The gradient estimate of a Neumann eigenfunction on a compact manifold with boundary ⋮ Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian ⋮ Uniform gradient estimates on manifolds with a boundary and applications

Cites Work

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• Eigenfunction and Bochner Riesz estimates on manifolds with boundary
• On the boundedness of functions of (pseudo-) differential operators on compact manifolds
• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
• On the convergence of Riesz means on compact manifolds
• The weak type \(L^ 1\) convergence of eigenfunction expansions for pseudodifferential operators
• Elliptic partial differential equations of second order
• Riemannian manifolds with maximal eigenfunction growth
• Plancherel-type estimates and sharp spectral multipliers
• On the \(L^p\) norm of spectral clusters for compact manifolds with boundary
• The spectral function of an elliptic operator
• Inequalities for strongly singular convolution operators
• UNIFORM BOUNDS FOR EIGENFUNCTIONS OF THE LAPLACIAN ON MANIFOLDS WITH BOUNDARY*
• Spectral cluster estimates for C 1,1 metrics
• New proof of the Hörmander multiplier theorem on compact manifolds without boundary
• Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem
• An Estimate Near the Boundary for the Spectral Function of the Laplace Operator
• Remarque sur la conjecture de Weyl.
• On the Critical Semilinear Wave Equation Outside Convex Obstacles

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