A logarithmic Hardy inequality

DOI10.1016/j.jfa.2010.06.005zbMath1209.26020arXiv0912.0590OpenAlexW2462606454MaRDI QIDQ992796

Jean Dolbeault, Stathis Filippas, Achilles Tertikas, Manuel A. del Pino

Publication date: 10 September 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0590

zbMATH Keywords

interpolationlogarithmic Sobolev inequalityscale invarianceSobolev inequalitysymmetry breakingHardy inequalityradial symmetryCaffarelli-Kohn-Nirenberg inequalitiesEmden-Fowler transformationHardy-Sobolev inequalities

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Linear function spaces and their duals (46E99) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (22)

Some trace Hardy type inequalities and trace Hardy-Sobolev-Maz'ya type inequalities ⋮ Optimal functional inequalities for fractional operators on the sphere and applications ⋮ Weighted interpolation inequalities: a perturbation approach ⋮ Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields ⋮ Rigidity results with applications to best constants and symmetry of Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities ⋮ Hardy-type inequalities for the Jacobi weight with applications ⋮ Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations ⋮ Anisotropic Shannon inequality ⋮ Improved Poincaré inequalities ⋮ Radial symmetry and symmetry breaking for some interpolation inequalities ⋮ A weighted Hardy type inequality and its applications ⋮ Hardy-type inequalities in arbitrary domains with finite inner radius ⋮ Sobolev and Hardy-Littlewood-Sobolev inequalities ⋮ On weighted logarithmic-Sobolev \& logarithmic-Hardy inequalities ⋮ On the Caffarelli-Kohn-Niremberg type inequalities and related topics ⋮ Weighted fast diffusion equations I: sharp asymptotic rates without symmetry and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities ⋮ Schrödinger-Newton equations in dimension two via a Pohozaev-Trudinger log-weighted inequality ⋮ Hardy-type inequalities with power and logarithmic weights in domains of the Euclidean space ⋮ Some Results Concerning Hardy and Hardy Type Inequalities ⋮ Generalizations of Hardy-type inequalities in the form of Dubinskii ⋮ Symmetry of extremals of functional inequalities via spectral estimates for linear operators ⋮ A review on some functional inequalities and symmetry properties of their external functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Convex Sobolev inequalities and spectral gap
• Best constants for Gagliardo-Nirenberg inequalities on the real line
• Gagliardo-Nirenberg inequalities involving the gradient \(L^2\)-norm
• Hardy inequalities with non-standard remainder terms
• Corrigendum to ``Optimizing improved Hardy inequalities [J. Funct. Anal. 192 (2002) 186-233]
• A new class of transport distances between measures
• On the best constant of Hardy-Sobolev inequalities
• Asymptotics of the fast diffusion equation via entropy estimates
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Best constant in weighted Sobolev inequality with weights being powers of distance from the origin
• Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
• Caffarelli--Kohn--Nirenberg inequalities with remainder terms.
• The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential
• A geometrical version of Hardy's inequality
• The optimal Euclidean \(L^{p}\)-Sobolev logarithmic inequality.
• Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type.
• Sharp two-sided heat kernel estimates for critical Schrödinger operators on bounded domains
• On existence of mimimizers for the Hardy-Sobolev-Maz'ya inequality
• Interpolation between logarithmic Sobolev and Poincaré inequalities
• On a question of Brezis and Marcus
• The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three-dimensional upper half space
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Some improved Caffarelli-Kohn-Nirenberg inequalities
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• An improved Hardy-Sobolev inequality and its application
• SYMMETRY BREAKING OF EXTREMAL FUNCTIONS FOR THE CAFFARELLI– KOHN–NIRENBERG INEQUALITIES
• On the Best Constant for a Weighted Sobolev-Hardy Inequality
• Improving L ² estimates to Harnack inequalities
• The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions
• On the symmetry of extremals for the Caffarelli-Kohn-Nirenberg inequalities
• Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.
• Logarithmic Sobolev Inequalities
• Logarithmic Sobolev Inequalities for the Heat-Diffusion Semigroup
• Sur l'inégalité logarithmique de Sobolev
• Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities
• On the best constant in a Hardy–Sobolev inequality
• Unified Poincaré and Hardy inequalities with sharp constants for convex domains
• Hardy's inequality with weights
• Hardy-type inequalities

This page was built for publication: A logarithmic Hardy inequality