INTERIOR NODAL SETS OF STEKLOV EIGENFUNCTIONS ON SURFACES

被引：13

作者：

Zhu, Jiuyi ^{[1
]}

机构：

[1] Johns Hopkins Univ, Dept Math, 313 Krieger Hall,3400 N Charles St, Baltimore, MD 21218 USA

来源：

ANALYSIS & PDE | 2016年 / 9卷 / 04期

基金：

美国国家科学基金会;

关键词：

nodal sets; upper bound; Steklov eigenfunctions; HAUSDORFF MEASURE; LOWER BOUNDS; EQUATIONS;

D O I：

10.2140/apde.2016.9.859

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the interior nodal sets N-lambda of Steklov eigenfunctions on connected and compact surfaces with boundary. The optimal vanishing order of Steklov eigenfunctions is shown be C lambda. The singular sets S-lambda consist of finitely many points on the nodal sets. We are able to prove that the Hausdorff measure H-0(S lambda) is at most C lambda(2). Furthermore, we obtain an upper bound for the measure of interior nodal sets, H-1(N-lambda) <= C lambda(3/2). Here the positive constants C depend only on the surfaces.

引用

页码：859 / 880

页数：22

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