Courant-sharp Robin eigenvalues for the square and other planar domains

DOI10.4171/PM/2027zbMath1444.35118arXiv1812.09344MaRDI QIDQ2335815

Katie Gittins, Bernard Helffer

Publication date: 15 November 2019

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.09344

zbMATH Keywords

squareplanar domainsCourant's nodal domain theoremCourant-sharpRobin eigenvalues

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (7)

Four end solutions of a free boundary problem ⋮ On Pleijel's nodal domain theorem for the Robin problem ⋮ Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter ⋮ Courant-sharp eigenvalues of compact flat surfaces: Klein bottles and cylinders ⋮ Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip ⋮ Courant-sharp Robin eigenvalues for the square and other planar domains ⋮ Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Faber-Krahn inequalities for the Robin-Laplacian: a free discontinuity approach
• Nodal sets for solutions of elliptic equations
• The nodal line of the second eigenfunction of the Robin Laplacian in \(\mathbb R^2\) can be closed
• A variational approach to the isoperimetric inequality for the Robin eigenvalue problem
• Nodal domains and spectral minimal partitions
• Nodal sets of eigenfunctions on Riemannian manifolds
• Membranes élastiquement liées inhomogènes ou sur une surface: Une nouvelle extension de théorème isopérimétrique de Rayleigh-Faber- Krahn. (Inhomogeneously or on a surface elastically supported membranes: A new extension of the isoperimetric theorem of Rayleigh-Faber-Krahn)
• Eigenfunctions and nodal sets
• Nodal sets for ground states of Schrödinger operators with zero magnetic field in non simply connected domains
• On the asymptotic behavior of the first eigenvalue of Robin problem with large parameter
• Bounds on the multiplicity of eigenvalues for fixed membranes
• Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter
• Sturm's theorem on zeros of linear combinations of eigenfunctions
• Courant-sharp Robin eigenvalues for the square and other planar domains
• Pleijel's nodal domain theorem for Neumann and Robin eigenfunctions
• A Faber-Krahn inequality for Robin problems in any space dimension
• On \(C^0\)-sufficiency of jets of potential functions
• Nodal domains in the square---the Neumann case
• Spectral Minimal Partitions for a Thin Strip on a Cylinder or a Thin Annulus like Domain with Neumann Condition
• Geometrical Structure of Laplacian Eigenfunctions
• Local behavior of solutions of general linear elliptic equations
• Remarks on courant's nodal line theorem
• Inégalités isopérimétriques et applications
• Dirichlet Eigenfunctions of the Square Membrane: Courant’s Property, and A. Stern’s and Å. Pleijel’s Analyses
• Nodal Sets for Eigenfunctions of the Laplacian On Surfaces
• An isoperimetric inequality for the second eigenvalue of the Laplacian with Robin boundary conditions
• Elliptic Partial Differential Equations of Second Order

This page was built for publication: Courant-sharp Robin eigenvalues for the square and other planar domains