The sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions

被引：9

作者：

Logunov, A. ^{[1
,2
]}

Malinnikova, E. ^{[3
,4
]}

Nadirashvili, N. ^{[5
]}

Nazarov, F. ^{[6
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Univ Geneva, Sect Math, Geneva, Switzerland

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[4] NTNU, Dept Math Sci, Trondheim, Norway

[5] CNRS, Inst Math Marseille, Marseille, France

[6] Kent State Univ, Dept Math, Kent, OH 44242 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2021年 / 31卷 / 05期

关键词：

Laplace eigenfunction; Nodal set; Lipschitz domain; UNIQUE CONTINUATION; DOMAINS;

D O I：

10.1007/s00039-021-00581-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Omega be a bounded domain in R-n with C-1 boundary and let u(lambda) be a Dirichlet Laplace eigenfunction in Omega with eigenvalue lambda. We show that the (n - 1)-dimensional Hausdorff measure of the zero set of u(lambda) does not exceed C(Omega)root lambda. This result is new even for the case of domains with C-infinity-smooth boundary.

引用

页码：1219 / 1244

页数：26

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