Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations
DOI10.3934/dcds.2022093arXiv2202.09693OpenAlexW4225301027MaRDI QIDQ6160079
Jean Dolbeault, Bruno Nazaret, Nikita Simonov, Matteo Bonforte
Publication date: 23 June 2023
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2202.09693
stabilityfast diffusion equationself-similar solutionsspectral gaprates of convergenceentropy methodsCaffarelli-Kohn-Nirenberg inequalityHarnack principleHardy-Poincaré inequalitiesGagliardo-Nirenberg-Sobolev inequality
Optimality conditions for problems involving partial differential equations (49K20) Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10)
Cites Work
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- Symmetry for extremal functions in subcritical Caffarelli-Kohn-Nirenberg inequalities
- Weighted fast diffusion equations I: sharp asymptotic rates without symmetry and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities
- Weighted fast diffusion equations II: sharp asymptotic rates of convergence in relative error by entropy methods
- The sharp Sobolev inequality in quantitative form
- A logarithmic Hardy inequality
- Asymptotics of the fast diffusion equation via entropy estimates
- Sobolev inequalities with remainder terms
- A note on the Sobolev inequality
- Best constant in Sobolev inequality
- Problèmes isoperimetriques et espaces de Sobolev
- Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
- Asymptotic behaviour for the porous medium equation posed in the whole space.
- Interpolation inequalities, nonlinear flows, boundary terms, optimality and linearization
- Quantitative a priori estimates for fast diffusion equations with Caffarelli-Kohn-Nirenberg weights. Harnack inequalities and Hölder continuity
- Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type.
- Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass Keller-Segel equation
- Reverse Hardy-Littlewood-Sobolev inequalities
- An extension of the Bianchi-Egnell stability estimate to Bakry, Gentil, and Ledoux's generalization of the Sobolev inequality to continuous dimensions
- Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces
- Extremal functions for Caffarelli—Kohn—Nirenberg and logarithmic Hardy inequalities
- Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
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