Improved Berezin-Li-Yau inequalities with a remainder term

zbMath1168.35404arXiv0711.4925MaRDI QIDQ3616121

Timo Weidl

Publication date: 24 March 2009

Full work available at URL: https://arxiv.org/abs/0711.4925

zbMATH Keywords

Weyl asymptoticsDirichlet LaplacianLieb-Thirring inequalitiesBerezin-type bounds

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Nonlinear elliptic equations (35J60)

Related Items (15)

The Lieb–Thirring inequalities: Recent results and open problems ⋮ Berezin-Li-Yau inequalities on domains on the sphere ⋮ A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions ⋮ Spectral estimates for Dirichlet Laplacians and Schrödinger operators on geometrically nontrivial cusps ⋮ Spectral estimates for the Dirichlet Laplacian on spiral-shaped regions ⋮ 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 ⋮ Comparison theorems for eigenvalues of elliptic operators and the generalized Pólya conjecture ⋮ 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 ⋮ An improvement to a Berezin-Li-Yau type inequality ⋮ Semiclassical bounds in magnetic bottles ⋮ Refined eigenvalue bounds on the Dirichlet fractional Laplacian

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