The diameter of the first nodal line of a convex domain

DOI10.2307/2118626zbMath0831.35115OpenAlexW2322763325MaRDI QIDQ1842581

David S. Jerison

Publication date: 15 February 1996

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2118626

zbMATH Keywords

bounds for eigenvaluesapproximation of membrane eigenfunctionslocation of a nodal line

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Connections of harmonic functions with differential equations in two dimensions (31A35)

Related Items (20)

On the number of critical points of the second eigenfunction of the Laplacian in convex planar domains ⋮ Locating the first nodal set in higher dimensions ⋮ Nodal sets of Laplace eigenfunctions under small perturbations ⋮ The nodal line of the second eigenfunction of the Laplacian in \(\mathbb{R}^2\) can be closed ⋮ Uniform Level Set Estimates for Ground State Eigenfunctions ⋮ The shape of the level sets of the first eigenfunction of a class of two-dimensional Schrödinger operators ⋮ Rebuttal of Donnelly's paper on the spectral gap ⋮ Spectral gap for convex planar domains ⋮ A counterexample to Payne's nodal line conjecture with few holes ⋮ The size of the first eigenfunction of a convex planar domain ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ Convergence of nodal sets in the adiabatic limit ⋮ Locating the first nodal linein the Neumann problem ⋮ A spectral gap estimate and applications ⋮ Nodal sets of thin curved layers ⋮ Nodal line estimates for the second Dirichlet eigenfunction ⋮ On the number of critical points of solutions of semilinear elliptic equations ⋮ A multiresolution strategy for reduction of elliptic PDEs and eigenvalue problems ⋮ Localisation of the first eigenfunction of a convex domain ⋮ The torsion function of convex domains of high eccentricity

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