Interior nodal sets of Steklov eigenfunctions on surfaces

2015/07/02 by Zhu, Jiuyi
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1507.00621

Abstract

We investigate the interior nodal sets N_λ of Steklov eigenfunctions on connected and compact surfaces with boundary. The optimal vanishing order of Steklov eigenfunctions is shown be Cλ. The singular sets S_λ are finite points on the nodal sets. We are able to prove that the Hausdorff measure H⁰(S_λ)≤ Cλ². Furthermore, we obtain an upper bound for the measure of interior nodal sets H¹(N_λ)≤ Cλ^(3)/(2). Here those positive constants C depend only on the surfaces.

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