The nodal surface of the second eigenfunction of the Laplacian in \(\mathbb{R}^D\) can be closed

DOI10.1006/jdeq.2000.3868zbMath1011.47033OpenAlexW2012653833MaRDI QIDQ5945595

Søren Fournais

Publication date: 9 June 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3868

zbMATH Keywords

Dirichlet Laplaciannodal surfacesecond eigenfunction

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) General theory of partial differential operators (47F05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (11)

On the Nodal set of a second Dirichlet eigenfunction in a doubly connected domain ⋮ On nodal line of the second eigenfunction of the Laplacian over concave domains in \(\mathbb R^2\) ⋮ A toy Neumann analogue of the nodal line conjecture ⋮ On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems ⋮ The nodal line of the second eigenfunction of the Robin Laplacian in \(\mathbb R^2\) can be closed ⋮ A counterexample to Payne's nodal line conjecture with few holes ⋮ Convergence of nodal sets in the adiabatic limit ⋮ Lieb-Thirring inequalities for geometrically induced bound states ⋮ Nodal sets of thin curved layers ⋮ On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations ⋮ On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains – with some numerics –

Cites Work

• On the nodal line of the second eigenfunction of the Laplacian in \(\mathbb{R}^ 2\)
• The nodal line of the second eigenfunction of the Laplacian in \(\mathbb{R}^2\) can be closed
• A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains
• Eigenfunctions of Laplace operators
• Isoperimetric Inequalities and Their Applications
• Potential theory for infinitely divisible processes on Abelian groups
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