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

共 23 条

[1] Adolfsson V, 1997, COMMUN PUR APPL MATH, V50, P935, DOI 10.1002/(SICI)1097-0312(199710)50:10<935::AID-CPA1>3.0.CO
[2] 2-H
[3] Adolfsson V, 1995, REV MAT IBEROAM, V11, P513
[4] Agmon S, 1966, SEMINAIRE MATH SUPER
[5] The stability for the Cauchy problem for elliptic equations
Alessandrini, Giovanni
Rondi, Luca
Rosset, Edi
Vessella, Sergio
[J]. INVERSE PROBLEMS, 2009, 25 (12)
[6] Almgren F. J., 1979, Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents, P1
[7] NODAL SETS OF EIGENFUNCTIONS ON RIEMANNIAN-MANIFOLDS
DONNELLY, H
FEFFERMAN, C
[J]. INVENTIONES MATHEMATICAE, 1988, 93 (01) : 161 - 183
[8] DONNELLY HAROLD, 1990, Nodal sets of eigenfunctions: Riemannian manifolds with boundary, Analysis, et cetera, P251
[9] Han Q, 2007, PURE APPL MATH Q, V3, P647
[10] LOGARITHMIC CONVEXITY FOR SUPREMUM NORMS OF HARMONIC-FUNCTIONS
KOREVAAR, J
MEYERS, JLH
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1994, 26 : 353 - 362

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