Improved Poincaré inequalities

DOI10.1016/j.na.2012.05.008zbMath1250.26018arXiv1111.1516OpenAlexW1995918022MaRDI QIDQ448505

Bruno Volzone, Jean Dolbeault

Publication date: 6 September 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.1516

zbMATH Keywords

Poincaré inequalityweighted normsHardy inequalitybest constantremainder terms

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Estimates of eigenvalues in context of PDEs (35P15) Functional equations for real functions (39B22) Functional inequalities, including subadditivity, convexity, etc. (39B62) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (11)

Hypercontractivity for Markov semi-groups ⋮ Remarks on the Rellich inequality ⋮ A unified divergent approach to Hardy-Poincaré inequalities in classical and variable Sobolev spaces ⋮ Large coupling in a FitzHugh-Nagumo neural network: quantitative and strong convergence results ⋮ Stochastic gradient descent with noise of machine learning type. II: Continuous time analysis ⋮ Hardy type inequalities with spherical derivatives ⋮ Improved Hardy inequalities with exact remainder terms ⋮ Hardy type inequalities in \(L^{p}\) with sharp remainders ⋮ \(\mathrm{L}^2\)-hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system ⋮ Some Hardy type inequalities with Finsler norms ⋮ Weighted Korn and Poincaré-Korn inequalities in the Euclidean space and associated operators

Cites Work

• Unnamed Item
• Unnamed Item
• Improved intermediate asymptotics for the heat equation
• Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
• On Hardy inequalities with a remainder term
• Fractional Poincaré inequalities for general measures
• Radial symmetry and symmetry breaking for some interpolation inequalities
• Fast diffusion equations: matching large time asymptotics by relative entropy methods
• An improved Hardy-Sobolev inequality in \(W^{1,p}\) and its application to Schrödinger operators
• Hardy-Poincaré inequalities and applications to nonlinear diffusions
• Corrigendum to ``Optimizing improved Hardy inequalities [J. Funct. Anal. 192 (2002) 186-233]
• Special fast diffusion with slow asymptotics: Entropy method and flow on a Riemannian manifold
• A logarithmic Hardy inequality
• On the best constant of Hardy-Sobolev inequalities
• Asymptotics of the fast diffusion equation via entropy estimates
• Hypocoercivity for kinetic equations with linear relaxation terms
• The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential
• Optimizing improved Hardy inequalities
• An analytical proof of Hardy-like inequalities related to the Dirac operator
• Extremal functions for Hardy's inequality with weight
• An improved Hardy-Sobolev inequality and its application
• Extremal functions for Caffarelli—Kohn—Nirenberg and logarithmic Hardy inequalities
• On the best possible remaining term in the Hardy inequality
• Logarithmic Sobolev Inequalities
• Series expansion for L^p Hardy inequalities
• A unified approach to improved $L^p$ Hardy inequalities with best constants
• Existence and non-existence of the first eigenvalue of the perturbed Hardy–Sobolev operator
• Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
• Hypocoercivity for linear kinetic equations conserving mass
• Many-particle Hardy inequalities

This page was built for publication: Improved Poincaré inequalities