A generalization of Courant's nodal domain theorem.

DOI10.7146/math.scand.a-10484zbMath0077.30101OpenAlexW2531755248MaRDI QIDQ3242362

Jaak Peetre

Publication date: 1957

Published in: MATHEMATICA SCANDINAVICA (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165645

zbMATH Keywords

partial differential equations, potential theory

Related Items (19)

Dirichlet Eigenfunctions of the Square Membrane: Courant’s Property, and A. Stern’s and Å. Pleijel’s Analyses ⋮ Extremals of determinants of Laplacians ⋮ Remarks on the boundary set of spectral equipartitions ⋮ Ein Eindeutigkeitssatz für Flächen konstanter mittlerer Krümmung ⋮ Nodal decompositions of graphs ⋮ Pleijel's nodal domain theorem for Neumann and Robin eigenfunctions ⋮ Upper bounds for Courant-sharp Neumann and Robin eigenvalues ⋮ On Pleijel's nodal domain theorem for the Robin problem ⋮ Inégalités isopérimétriques et applications ⋮ Pleijel's theorem for Schrödinger operators with radial potentials ⋮ The weak Pleijel theorem with geometric control ⋮ Courant-sharp eigenvalues of compact flat surfaces: Klein bottles and cylinders ⋮ A. Stern's analysis of the nodal sets of some families of spherical harmonics revisited ⋮ Describing the singular behaviour of parabolic equations on cones in fractional Sobolev spaces ⋮ Über Knoten von Eigenfunktionen des Laplace-Beltrami-Operators ⋮ Pleijel’s nodal domain theorem for free membranes ⋮ Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip ⋮ On nodal domains in Euclidean balls ⋮ Stability of minimal surfaces and eigenvalues of the Laplacian

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