On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains - with some numerics -

被引：0

作者：

Helffer, B. ^{[1
,2
]}

Hoffmann-Ostenhof, T. ^{[3
]}

Jauberteau, F. ^{[1
]}

Lena, C. ^{[4
]}

机构：

[1] Univ Nantes, Lab Mathemat Jean Leray, Nantes, France

[2] Univ Paris Sud, Lab Math Orsay, Paris, France

[3] Univ Wien, Inst Theoret Chem, Vienna, Austria

[4] Univ Stockholm, Dept Math, Stockholm, Sweden

来源：

ASYMPTOTIC ANALYSIS | 2020年 / 121卷 / 01期

基金：

瑞典研究理事会;

关键词：

Spectral theory; Laplacian; multiplicity; EIGENFUNCTIONS;

D O I：

10.3233/ASY-191594

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in R-2 for which the second eigenvalue of the Dirichlet Laplacian has multiplicity 3. We also analyze carefully the first eigenvalues of the Laplacian in the case of the disk with two symmetric cracks placed on a smaller concentric disk in function of their size.

引用

页码：35 / 57

页数：23

共 41 条

[21] An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane
Nikolai S. Nadirashvili
Alexei V. Penskoi
Geometric and Functional Analysis, 2018, 28 : 1368 - 1393
[22] Ginzburg-Landau equation with magnetic effect: non-simply-connected domains
Jimbo, S
Zhai, J
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1998, 50 (03) : 663 - 684
[23] On the least signless Laplacian eigenvalue of a non-bipartite connected graph with fixed maximum degree
Shu-Guang Guo
Rong Zhang
Journal of Inequalities and Applications, 2017
[24] On the least signless Laplacian eigenvalue of a non-bipartite connected graph with fixed maximum degree
Guo, Shu-Guang
Zhang, Rong
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
[25] Existence and multiplicity of periodic solutions for some second order differential systems with p(t)-Laplacian
Zhang, Liang
Tang, X. H.
MATHEMATICA SLOVACA, 2013, 63 (06) : 1269 - 1290
[26] NON-SIMPLY-CONNECTED SURGERY AND SOME RESULTS IN LOW DIMENSIONAL TOPOLOGY
SHANESON, JL
COMMENTARII MATHEMATICI HELVETICI, 1970, 45 (03) : 333 - &
[27] Nodal sets for groundstates of Schrodinger operators with zero magnetic field in non simply connected domains
Helffer, B
Hoffmann-Ostenhof, M
Hoffmann-Ostenhof, T
Owen, MP
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 202 (03) : 629 - 649
[28] NONLINEAR EIGENVALUE PROBLEM DELTA-U+LAMBDA-E(U)=0 ON SIMPLY CONNECTED DOMAINS IN R2
SUZUKI, T
NAGASAKI, K
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1989, 65 (01) : 1 - 3
[29] Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains
B. Helffer
M. Hoffmann-Ostenhof
T. Hoffmann-Ostenhof
M. P. Owen
Communications in Mathematical Physics, 1999, 202 : 629 - 649
[30] Existence and non existence results for supercritical systems of Liouville-type equations on simply connected domains
Daniele Bartolucci
Calculus of Variations and Partial Differential Equations, 2015, 53 : 317 - 348

← 1 2 3 4 5 →