Hardy-Poincaré inequalities and applications to nonlinear diffusions

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Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincar\'e inequalities (2012, unknown): “The papers [7], [8] show that the zero-mean Poincaré inequality ‖v − v‖2;ν ≤MP ‖∇v‖2;μ is valid in the appropriate Sobolev space if and only if α < 1 −N/2.”
Hypocoercivity for kinetic equations with linear relaxation terms (2008, background): “En introduisant de nouveaux opérateurs, nous améliorons et nous simplifions les résultats antérieurs, tout en mettant en évidence la relaxation à l’échelle microscopique due au terme de collision, ici un opérateur de relaxation linéaire, et la relaxation à l’échelle macroscopique, qui vient d’une pr”
Special Fast Diffusion with Slow Asymptotics: Entropy Method and Flow on a Riemannian Manifold (2008, methodology): “1) F [g(s)] ≤ λ m,d I[g(s)] holds true, and the best constant is known for m < m∗, since [4, 5].”
Weighted poincaré-type inequalities for cauchy and other convex measures (2009, background): “After this work was completed, we became aware of the related references [2, 3], where some similar inequalities are proved and analyzed by different methods and with different purposes.”
Bessel pairs and optimal Hardy and Hardy–Rellich inequalities (2011, result): “We can also extend some of the recent results of Blanchet et al. [ 6 ].”