Elsevier, Comptes Rendus Mathématique, 7(344), p. 431-436
DOI: 10.1016/j.crma.2007.01.011
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We systematically study weighted Poincaré type inequalities which are closely connected with Hardy type inequalities and establish the form of the optimal constants in some cases. Such inequalities are then used to relate entropy with entropy production and get intermediate asymptotics results for fast diffusion equations.