A spectral gap estimate and applications

DOI10.1007/s11118-017-9670-6zbMath1400.35192arXiv1612.08565OpenAlexW2588413686MaRDI QIDQ1787166

Mayukh Mukherjee, Stefan Steinerberger, Bogdan Georgiev

Publication date: 4 October 2018

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.08565

zbMATH Keywords

Schrödinger operatorground stateconvex domainLaplacian eigenfunction

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Eigenvalue problems for linear operators (47A75) Schrödinger operator, Schrödinger equation (35J10)

Related Items (2)

Location of maximizers of eigenfunctions of fractional Schrödinger's equations ⋮ Localisation of the first eigenfunction of a convex domain

Cites Work

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• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• A reverse Hölder inequality for the eigenfunctions of linear second order elliptic operators
• On the \(L^\infty\) norm of the first eigenfunction of the Dirichlet Laplacian
• The diameter of the first nodal line of a convex domain
• Bounds on the eigenvalues of the Laplace and Schroedinger operators
• The size of the first eigenfunction of a convex planar domain

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