Functional inequalities: nonlinear flows and entropy methods as a tool for obtaining sharp and constructive results
type: Item
instance of: scholarly article
title: Functional inequalities: nonlinear flows and entropy methods as a tool for obtaining sharp and constructive results
zbMATH Open document ID: 1481.35006
author: Jean Dolbeault
published in: Milan Journal of Mathematics
publication date: 2022-01-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/2107.08219
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35A23
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 35B06
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49K30
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 7462038
zbMATH Keywords: interpolation
zbMATH Keywords: Gagliardo-Nirenberg inequality
zbMATH Keywords: Caffarelli-Kohn-Nirenberg inequality
zbMATH Keywords: entropy methods
zbMATH Keywords: carré du champ
zbMATH Keywords: fast diffusion equation
zbMATH Keywords: Harnack principle
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: Hardy-Poincaré inequalities
zbMATH Keywords: spectral gap
zbMATH Keywords: intermediate asymptotics
zbMATH Keywords: self-similar Barenblatt solutions
zbMATH Keywords: rates of convergence
zbMATH Keywords: symmetry
zbMATH Keywords: symmetry breaking
zbMATH Keywords: bifurcation
zbMATH Keywords: entropy-entropy production inequalities
MaRDI profile type: Publication
OpenAlex ID: W3208760044
arXiv ID: 2107.08219
cites work: \(\mathrm{L}^2\)-hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system
cites work: Interpolation between logarithmic Sobolev and Poincaré inequalities
cites work: ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
cites work: Problèmes isoperimetriques et espaces de Sobolev
cites work: Q3676923
cites work: Q5186515
cites work: Analysis and Geometry of Markov Diffusion Operators
cites work: Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
cites work: Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
cites work: Q3142976
cites work: A note on the Sobolev inequality
cites work: Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
cites work: Asymptotics of the fast diffusion equation via entropy estimates
cites work: Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
cites work: Weighted fast diffusion equations I: sharp asymptotic rates without symmetry and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities
cites work: Weighted fast diffusion equations II: sharp asymptotic rates of convergence in relative error by entropy methods
cites work: Quantitative a priori estimates for fast diffusion equations with Caffarelli-Kohn-Nirenberg weights. Harnack inequalities and Hölder continuity
cites work: Global positivity estimates and Harnack inequalities for the fast diffusion equation
cites work: Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields
cites work: Inequalities involving Aharonov–Bohm magnetic potentials in dimensions 2 and 3
cites work: Hypocoercivity and sub-exponential local equilibria
cites work: Hypocoercivity without confinement
cites work: Diffusion and kinetic transport with very weak confinement
cites work: A variational proof of Nash's inequality
cites work: A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
cites work: Sobolev inequalities with remainder terms
cites work: Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
cites work: Q3676658
cites work: On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions.
cites work: Entropies, convexity, and functional inequalities: on \(\Phi\)-entropies and \(\Phi\)-Sobolev inequalities
cites work: Q3244064
cites work: On the Best Constant for a Weighted Sobolev-Hardy Inequality
cites work: The sharp Sobolev inequality in quantitative form
cites work: Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
cites work: A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
cites work: Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
cites work: The Euclidean Onofri Inequality in Higher Dimensions
cites work: Improved Gagliardo-Nirenberg-Sobolev inequalities on manifolds with positive curvature
cites work: Les espaces du type de Beppo Levi

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cites work: Sobolev and Hardy-Littlewood-Sobolev inequalities: duality and fast diffusion

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cites work: A scenario for symmetry breaking in Caffarelli–Kohn–Nirenberg inequalities

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cites work: Branches of non-symmetric critical points and symmetry breaking in nonlinear elliptic partial differential equations

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cites work: Improved interpolation inequalities and stability

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cites work: Improved interpolation inequalities on the sphere

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cites work: Nonlinear flows and rigidity results on compact manifolds

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cites work: Interpolation inequalities, nonlinear flows, boundary terms, optimality and linearization

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cites work: Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces

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cites work: Interpolation inequalities on the sphere: linear vs. nonlinear flows

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cites work: SYMMETRY AND SYMMETRY BREAKING: RIGIDITY AND FLOWS IN ELLIPTIC PDES

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cites work: Symmetry for extremal functions in subcritical Caffarelli-Kohn-Nirenberg inequalities

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cites work: Sobolev and Hardy-Littlewood-Sobolev inequalities

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cites work: φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations

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cites work: Hypocoercivity for linear kinetic equations conserving mass

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cites work: On the Bakry-Emery criterion for linear diffusions and weighted porous media equations

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cites work: Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type.

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cites work: Gradient stability for the Sobolev inequality: the case \(p\geq 2\)

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cites work: Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential

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cites work: Proprietà di alcune classi di funzioni in più variabili

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cites work: Global and local behavior of positive solutions of nonlinear elliptic equations

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cites work: Elliptic partial differential equations of second order

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cites work: Q3972863

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cites work: Best constant in weighted Sobolev inequality with weights being powers of distance from the origin

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cites work: Q3286578

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cites work: The Variational Formulation of the Fokker--Planck Equation

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cites work: Entropy Methods for Diffusive Partial Differential Equations

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cites work: Rearrangements and convexity of level sets in PDE

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cites work: Q5480316

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cites work: Q2702147

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cites work: Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

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cites work: Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities

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cites work: Analysis.

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cites work: A harnack inequality for parabolic differential equations

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cites work: On a pointwise estimate for parabolic differential equations

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cites work: Continuity of Solutions of Parabolic and Elliptic Equations

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cites work: A note on strong-form stability for the Sobolev inequality

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cites work: Q3260749

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cites work: THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION

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cites work: Minimum Value for c in the Sobolev Inequality $\| {\phi ^3 } \|\leqq c\| {\nabla \phi } \|^3 $

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cites work: The Concavity of Rényi Entropy Power

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cites work: Partial symmetry and asymptotic behavior for some elliptic variational problems

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cites work: Best constant in Sobolev inequality

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cites work: Q4108681

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cites work: Q4839442

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cites work: Hypocoercivity

Functional inequalities: nonlinear flows and entropy methods as a tool for obtaining sharp and constructive results (DOI)
DOI: 10.1007/S00032-021-00341-Y