Hausdorff measure bound for the nodal sets of Neumann Laplace eigenfunctions

2023/11/16 by Fazliani, Shaghayegh
#35P30 #42B37 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2311.09686

Abstract

We study the nodal sets of Neumann Laplace eigenfunctions in a bounded domain with C^1,1 boundary. We show that for u_λ such that Δu_λ+ λu_λ= 0 with the Neumann boundary condition ∂_νu_λ= 0, we have H^n-1(\u_λ= 0\) ≤ C √λ.

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