Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem

DOI10.1515/FORUM.2009.021zbMath1171.35442MaRDI QIDQ3632756

Xiangjin Xu

Publication date: 12 June 2009

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

zbMATH Keywords

Riemannian manifoldseigenfunctionsDirichlet Laplaciangradient estimatesHörmander multiplier theorem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) A priori estimates in context of PDEs (35B45) Boundary value problems on manifolds (58J32)

Related Items (16)

Gradient estimate of an eigenfunction on a compact Riemannian manifold without boundary ⋮ Fractional Brownian fields over manifolds ⋮ Coefficient identification in parabolic equations with final data ⋮ Boundedness of spectral multipliers of generalized Laplacians on compact manifolds with boundary ⋮ Non‐harmonic Gohberg's lemma, Gershgorin theory and heat equation on manifolds with boundary ⋮ Scaling limit of the Fleming-Viot multicolor process ⋮ A pointwise inequality for derivatives of solutions of the heat equation in bounded domains ⋮ 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 ⋮ Quantum ergodicity and \(L^{p}\) norms of restrictions of eigenfunctions ⋮ Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary ⋮ Uniform gradient estimates on manifolds with a boundary and applications ⋮ Fractional Cauchy problems on compact manifolds ⋮ Lower bounds for interior nodal sets of Steklov eigenfunctions ⋮ Eigenfunction estimates for Neumann Laplacian and applications to multiplier problems ⋮ New proof of the Hörmander multiplier theorem on compact manifolds without boundary

Cites Work

• 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
• Riemannian manifolds with maximal eigenfunction growth
• Plancherel-type estimates and sharp spectral multipliers
• UNIFORM BOUNDS FOR EIGENFUNCTIONS OF THE LAPLACIAN ON MANIFOLDS WITH BOUNDARY*
• New proof of the Hörmander multiplier theorem on compact manifolds without boundary
• An Estimate Near the Boundary for the Spectral Function of the Laplace Operator
• On the Critical Semilinear Wave Equation Outside Convex Obstacles

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