Lieb-Thirring inequalities with improved constants

DOI10.4171/JEMS/142zbMath1152.35451arXiv0708.1165MaRDI QIDQ952517

Michael Loss, A. A. Laptev, Jean Dolbeault

Publication date: 12 November 2008

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.1165

zbMATH Keywords

Schrödinger operatorSobolev inequalitiesLieb-Thirring inequalities

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (38)

The Lieb–Thirring inequalities: Recent results and open problems ⋮ On the spectrum of the Stokes operator ⋮ Upper bounds for the attractor dimension of damped Navier-Stokes equations in \(\mathbb R^2\) ⋮ A proof of the Lieb-Thirring inequality via the Besicovitch covering lemma ⋮ Lieb-Thirring inequalities on the torus ⋮ Lieb–Thirring inequalities on the sphere ⋮ Number of eigenvalues of non-self-adjoint Schrödinger operators with dilation analytic complex potentials ⋮ Lieb-Thirring inequalities on some manifolds ⋮ Lieb-Thirring inequality with semiclassical constant and gradient error term ⋮ Magnetic Lieb-Thirring inequalities on the torus ⋮ A positive density analogue of the Lieb-Thirring inequality ⋮ Lieb-Thirring inequalities on manifolds with constant negative curvature ⋮ Cwikel's bound reloaded ⋮ Sums of magnetic eigenvalues are maximal on rotationally symmetric domains ⋮ Lieb-Thirring constant on the sphere and on the torus ⋮ Stability and absence of binding for multi-polaron systems ⋮ On some sharp spectral inequalities for Schrödinger operators on semiaxis ⋮ Binding of atoms in Müller theory ⋮ Hardy-Lieb-Thirring inequalities for fractional Pauli operators ⋮ New constants in discrete Lieb-Thirring inequalities for Jacobi matrices ⋮ Best constants in Lieb-Thirring inequalities: a numerical investigation ⋮ Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field ⋮ Sharp interpolation inequalities for discrete operators ⋮ Interpolation inequalities and spectral estimates for magnetic operators ⋮ Number of bound states of Schrödinger operators with matrix-valued potentials ⋮ Local exclusion and Lieb-Thirring inequalities for intermediate and fractional statistics ⋮ New bounds on the maximum ionization of atoms ⋮ Spectral inequalities for Jacobi operators and related sharp Lieb-Thirring inequalities on the continuum ⋮ Spectral bounds for polydiagonal Jacobi matrix operators ⋮ Convergence of Levy-Lieb to Thomas-Fermi density functional ⋮ A remark on the dimension of the attractor for the Dirichlet problem of the complex Ginzburg–Landau equation ⋮ The Lieb-Thirring inequality revisited ⋮ On the Lieb-Thirring constant on the torus ⋮ Lower bounds for sums of eigenvalues of elliptic operators and systems ⋮ On factorisation of a class of Schrödinger operators ⋮ Sums of Laplace eigenvalues: Rotations and tight frames in higher dimensions ⋮ Sharp interpolation inequalities for discrete operators and applications ⋮ Lieb-Thirring inequality for a model of particles with point interactions

Cites Work

• Unnamed Item
• Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
• A simple proof of the generalized Lieb-Thirring inequalities in one-space dimension
• New bounds on the Lieb-Thirring constants
• A simple proof of a theorem of Laptev and Weidl
• Sharp Lieb-Thirring inequalities in high dimensions.

This page was built for publication: Lieb-Thirring inequalities with improved constants