Hardy-Poincaré inequalities and applications to nonlinear diffusions
From MaRDI portal
Publication:877984
DOI10.1016/j.crma.2007.01.011zbMath1190.35119OpenAlexW1984130328MaRDI QIDQ877984
Jean Dolbeault, Matteo Bonforte, Adrien Blanchet, Gabriele Grillo, Juan Luis Vazquez
Publication date: 4 May 2007
Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.crma.2007.01.011
Reaction-diffusion equations (35K57) A priori estimates in context of PDEs (35B45) Inequalities for sums, series and integrals (26D15)
Related Items
Weighted interpolation inequalities: a perturbation approach, Improved intermediate asymptotics for the heat equation, Score functions, generalized relative Fisher information and applications, A unified divergent approach to Hardy-Poincaré inequalities in classical and variable Sobolev spaces, Progress in the Theory of Nonlinear Diffusion: Asymptotics via Entropy Methods, Bessel pairs and optimal Hardy and Hardy-Rellich inequalities, On Gilles Pisier's approach to Gaussian concentration, isoperimetry, and Poincaré-type inequalities, Functional inequalities and applications to doubly nonlinear diffusion equations, Poincaré-type inequalities for stable densities, Chemotaxis and reactions in biology, Large time asymptotics of the doubly nonlinear equation in the non-displacement convexity regime, Fine properties of solutions to the Cauchy problem for a fast diffusion equation with Caffarelli-Kohn-Nirenberg weights, Quantitative fluid approximation in transport theory: a unified approach, Improved Poincaré inequalities, Improved interpolation inequalities, relative entropy and fast diffusion equations, Behaviour near extinction for the fast diffusion equation on bounded domains, Liouville theorems for elliptic problems in variable exponent spaces, Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities, Functional aspects of the Hardy inequality: appearance of a hidden energy, Hardy inequalities resulted from nonlinear problems dealing with \(A\)-Laplacian, Special fast diffusion with slow asymptotics: Entropy method and flow on a Riemannian manifold, Convex Sobolev inequalities derived from entropy dissipation, 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, A family of Beckner inequalities under various curvature-dimension conditions, Asymptotics of the fast diffusion equation via entropy estimates, Hypocoercivity for kinetic equations with linear relaxation terms, Weighted Poincaré-type inequalities for Cauchy and other convex measures, Modified log-Sobolev inequalities, Beckner inequalities and moment estimates, \(\Phi\)-entropy inequalities and asymmetric covariance estimates for convex measures, Caccioppoli-type estimates and Hardy-type inequalities derived from weighted \(p\)-harmonic problems, Hypocoercivity for linear kinetic equations conserving mass, Higher-order time asymptotics of fast diffusion in Euclidean space: A dynamical systems approach
Cites Work
- Unnamed Item
- Unnamed Item
- Global positivity estimates and Harnack inequalities for the fast diffusion equation
- Asymptotics of the fast diffusion equation via entropy estimates
- Explicit constants for Rellich inequalities in \(L_p(\Omega)\)
- On Persson's theorem in local Dirichlet spaces
- Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
- Sobolev-Orlicz imbeddings, weak compactness, and spectrum
- Fast diffusion to self-similarity: Complete spectrum, long-time asymptotics, and numerology
- Integral inequalities and theorems of Liouville type
- Poincaré inequalities for linearizations of very fast diffusion equations
- On the extinction profile of solutions to fast diffusion
- Fine Asymptotics for Fast Diffusion Equations
- Bounds for the Discrete Part of the Spectrum of a Semi-Bounded Schrödinger Operator.
- Hardy's inequality with weights