On the number of Courant-sharp Dirichlet eigenvalues

Michiel van den Berg; Katie Gittins

doi:10.4171/JST/139

On the number of Courant-sharp Dirichlet eigenvalues

Michiel van den Berg, Katie Gittins

Research output: Contribution to journal › Article (Academic Journal) › peer-review

5 Citations (Scopus)

364 Downloads (Pure)

Abstract

We consider arbitrary open sets Ω in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of Ω, (ii) the number of Courant-sharp Dirichlet eigenvalues of Ω. This extends recent results of P. Bérard and B. Helffer.

Original language	English
Pages (from-to)	735-745
Number of pages	11
Journal	Journal of Spectral Theory
Volume	6
Issue number	4
DOIs	https://doi.org/10.4171/JST/139
Publication status	Published - 9 Dec 2016

Keywords

Weyl's theorem
Pleijel's theorem
Dirichlet Laplacian
Nodal domain

Access to Document

10.4171/JST/139

Full-text PDF (accepted author manuscript)
This is the accepted author manuscript (AAM). The final published version (version of record) is available online via European Mathematical Society at DOI: 10.4171/JST/139. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 366 KBLicence: Unspecified

Handle.net

Persistent link

Emeritus Professor Michiel van den Berg
- M.vandenBergbristol.acuk
- School of Mathematics - Emeritus Professor
- Probability, Analysis and Dynamics
- Pure Mathematics
- Analysis
Person: Member, Honorary and Visiting Academic

Cite this

@article{203156bf997a445d90e8a6346088f1a2,

title = "On the number of Courant-sharp Dirichlet eigenvalues",

abstract = "We consider arbitrary open sets Ω in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of Ω, (ii) the number of Courant-sharp Dirichlet eigenvalues of Ω. This extends recent results of P. B{\'e}rard and B. Helffer.",

keywords = "Weyl's theorem, Pleijel's theorem, Dirichlet Laplacian, Nodal domain",

author = "\{van den Berg\}, Michiel and Katie Gittins",

year = "2016",

month = dec,

day = "9",

doi = "10.4171/JST/139",

language = "English",

volume = "6",

pages = "735--745 ",

journal = "Journal of Spectral Theory",

issn = "1664-039X",

publisher = "European Mathematical Society",

number = "4",

}

TY - JOUR

T1 - On the number of Courant-sharp Dirichlet eigenvalues

AU - van den Berg, Michiel

AU - Gittins, Katie

PY - 2016/12/9

Y1 - 2016/12/9

N2 - We consider arbitrary open sets Ω in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of Ω, (ii) the number of Courant-sharp Dirichlet eigenvalues of Ω. This extends recent results of P. Bérard and B. Helffer.

AB - We consider arbitrary open sets Ω in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of Ω, (ii) the number of Courant-sharp Dirichlet eigenvalues of Ω. This extends recent results of P. Bérard and B. Helffer.

KW - Weyl's theorem

KW - Pleijel's theorem

KW - Dirichlet Laplacian

KW - Nodal domain

U2 - 10.4171/JST/139

DO - 10.4171/JST/139

M3 - Article (Academic Journal)

SN - 1664-039X

VL - 6

SP - 735

EP - 745

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 4

ER -

On the number of Courant-sharp Dirichlet eigenvalues

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Profiles

Emeritus Professor Michiel van den Berg

Cite this