On Pleijel's Nodal Domain Theorem

Jean Bourgain

Type: Article

Publication Date: 2013-12-18

Citations: 33

DOI: https://doi.org/10.1093/imrn/rnt241

Abstract

A slight improvement of Pleijel's estimate on the number of nodal domains is obtained, exploiting a refinement of the Faber–Krahn inequality and packing density of disks.

Locations

International Mathematics Research Notices - View
arXiv (Cornell University) - View - PDF

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+	Pleijel nodal domain theorem in non-smooth setting	2024	Nicolò De Ponti Sara Farinelli Ivan Yuri Violo
+	Quantum graphs -- Generic eigenfunctions and their nodal count and Neumann count statistics	2020	Lior Alon
+	Some nodal properties of the quantum harmonic oscillator and other Schr{ö}dinger operators in $\mathbb{R}^2$	2015	Pierre Bérard Bernard Helffer
+ PDF Chat	Nodal Decompositions of a Symmetric Matrix	2024	Theo McKenzie John Urschel
+ PDF Chat	A Geometric Uncertainty Principle with an Application to Pleijel’s Estimate	2013	Stefan Steinerberger
+ PDF Chat	Large m asymptotics for minimal partitions of the Dirichlet eigenvalue	2021	Zhiyuan Geng Fanghua Lin
+	On exact Pleijel's constant for some domains	2018	Vladimir Bobkov
+ PDF Chat	Quantitative projections in the Sturm Oscillation Theorem	2020	Stefan Steinerberger
+ PDF Chat	Pleijel’s theorem for Schrödinger operators with radial potentials	2017	Philippe Charron Bernard Helffer Thomas Hoffmann-Ostenhof
+ PDF Chat	On the number of Courant-sharp Dirichlet eigenvalues	2016	M. van den Berg Katie Gittins

Works Cited by This (12)

Action	Title	Year	Authors
+ PDF Chat	Random wavefunctions and percolation	2007	E. Bogomolny C. Schmit
+ PDF Chat	Nodal domains and spectral minimal partitions	2007	Susanna Terracini Bernard Helffer Thomas Hoffmann-Ostenhof
+	Isoperimetric Inequalities in Potential Theory	1994	Wolfhard Hansen Nikolaï Nadirashvili
+	On Spectral Minimal Partitions: A Survey	2010	Bernard Helffer
+ PDF Chat	On the number of nodal domains of random spherical harmonics	2009	Fëdor Nazarov Mikhail Sodin
+	Some observations on the first eigenvalue of the -Laplacian and its connections with asymmetry.	2001	Tilak Bhattacharya
+	Existence and analyticity of a parabolic evolution operator for nonautonomous linear equations in Banach spaces	2009	Antonio Sergio Munhoz Antônio Calixto de Souza Filho
+ PDF Chat	On nodal sets and nodal domains on \mathbf{S^2} and {\mathbb{R}}^{\mathbf{2}}	2007	Alexandre Erëmenko Dmitry Jakobson Nikolaï Nadirashvili
+ PDF Chat	Pleijel’s nodal domain theorem for free membranes	2008	Iosif Polterovich
+	Asymptotic Statistics of Nodal Domains of Quantum Chaotic Billiards in the Semiclassical Limit	2012	Kyle T Konrad