Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

2010/04/14 by Xiangjin Xu, Xu, Xiangjin · 1 citation
Computer Science · Mathematics · #35J25 #35R01 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Primary 35P20 #Secondary 58J40 #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1004.2517

openalex publication_date 2010/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the upper and lower bounds for normal derivatives of spectral clusters u=χ_λ^s f of Dirichlet Laplacian Δ_M, c_s λ‖u‖_L²(M) ≤ ‖ ∂_νu ‖_{L²(∂ M)} ≤ C_s λ‖u‖_L²(M) where the upper bound is true for any Riemannian manifold, and the lower bound is true for some small 0

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• Estimates of Eigenvalues and Eigenfunctions in Periodic Homogenization

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