LOWER BOUNDS FOR INTERIOR NODAL SETS OF STEKLOV EIGENFUNCTIONS

被引：12

作者：

Sogge, Christopher D. ^{[1
]}

Wang, Xing ^{[1
,2
]}

Zhu, Jiuyi ^{[1
,3
]}

机构：

[1] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[3] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 11期

基金：

美国国家科学基金会;

关键词：

COMPACT MANIFOLDS; HAUSDORFF MEASURE; OPERATORS;

D O I：

10.1090/proc/13067

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the interior nodal sets, Z(lambda) of Steklov eigenfunctions in an n-dimensional relatively compact manifold M with boundary and show that one has the lower bounds vertical bar Z(lambda)vertical bar = c(lambda) 2-n/2 2 for the size of its (n -1)-dimensional Hausdorff measure. The proof is based on a Dong-type identity and estimates for the gradient of Steklov eigenfunctions, similar to those in previous works of the first author and Zelditch.

引用

页码：4715 / 4722

页数：8

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