Fractional Hardy-Lieb-Thirring and related inequalities for interacting systems

DOI10.1007/s00205-015-0923-5zbMath1332.81292arXiv1501.04570OpenAlexW3104796331MaRDI QIDQ5962888

Fabian Portmann, Phan Thành Nam, Douglas Lundholm

Publication date: 25 February 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.04570

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Fractional derivatives and integrals (26A33) Many-body theory; quantum Hall effect (81V70) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (18)

The Lieb–Thirring inequalities: Recent results and open problems ⋮ Fermionic behavior of ideal anyons ⋮ Statistical mechanics of the uniform electron gas ⋮ Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg interpolation inequalities associated with Coulomb-Sobolev spaces ⋮ Sharp Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces ⋮ A proof of the Lieb-Thirring inequality via the Besicovitch covering lemma ⋮ Hardy-Sobolev inequalities with Dunkl weights ⋮ Lieb-Thirring inequality with semiclassical constant and gradient error term ⋮ Critical conditions and asymptotics for discrete systems of the Hardy-Littlewood-Sobolev type ⋮ Exclusion bounds for extended anyons ⋮ Next-order asymptotic expansion for \(N\)-marginal optimal transport with Coulomb and Riesz costs ⋮ Euler-Lagrange equations associated with extremal functions of several nonlocal inequalities ⋮ Asymptotic behavior for the quasi-geostrophic equations with fractional dissipation in \(\mathbb{R}^2\) ⋮ Triviality of a model of particles with point interactions in the thermodynamic limit ⋮ The Lieb-Thirring inequality for interacting systems in strong-coupling limit ⋮ Lieb-Thirring inequalities for wave functions vanishing on the diagonal set ⋮ Lieb-Thirring bounds for interacting Bose gases ⋮ A Lieb-Thirring inequality for extended anyons

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