Geometrical versions of improved Berezin-Li-Yau inequalities

DOI10.4171/JST/4zbMath1257.35138arXiv1010.2683MaRDI QIDQ1933407

Leander Geisinger, Timo Weidl, A. A. Laptev

Publication date: 23 January 2013

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.2683

zbMATH Keywords

semiclassical estimatesDirichlet Laplace operatorBerezin-Li-Yau inequality

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Eigenvalue problems for linear operators (47A75)

Related Items (18)

The Lieb–Thirring inequalities: Recent results and open problems ⋮ Two-term, asymptotically sharp estimates for eigenvalue means of the Laplacian ⋮ A bound for the perimeter of inner parallel bodies ⋮ Berezin-Li-Yau inequalities on domains on the sphere ⋮ A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions ⋮ Eigenvalue bounds of mixed Steklov problems ⋮ Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain ⋮ Semiclassical estimates for eigenvalue means of Laplacians on spheres ⋮ On the remainder term of the Berezin inequality on a convex domain ⋮ Sums of magnetic eigenvalues are maximal on rotationally symmetric domains ⋮ Hardy-Sobolev-Maz'ya inequalities for arbitrary domains ⋮ A remark on Pólya's conjecture at low frequencies ⋮ Sharper estimates on the eigenvalues of Dirichlet fractional Laplacian ⋮ A short proof of Weyl's law for fractional differential operators ⋮ Lower bounds for sums of eigenvalues of elliptic operators and systems ⋮ Refined eigenvalue bounds on the Dirichlet fractional Laplacian ⋮ Sums of Laplace eigenvalues: Rotations and tight frames in higher dimensions ⋮ Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains

Cites Work

• Lieb-Thirring inequalities for geometrically induced bound states
• On Lieb-Thirring inequalities for Schrödinger operators with virtual level
• Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
• Spectral inequalities for Schroedinger operators with surface potentials
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