Improved Sobolev's inequalities, relative entropy and fast diffusion equations - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

Improved Sobolev's inequalities, relative entropy and fast diffusion equations

Résumé

The difference of the two terms in Sobolev's inequality (with optimal constant) measures a distance to the manifold of the optimal functions. We give an explicit estimate of the remainder term and establish an improved inequality, with explicit norms and fully detailed constants. Our approach is based on nonlinear evolution equations and improved entropy - entropy production estimates along the associated flow. Optimizing a relative entropy functional with respect to a scaling parameter, or handling properly second moment estimates, turns out to be the central technical issue. This is a new method in the theory of nonlinear evolution equations, which also applies to other interpolation inequalities of Gagliardo-Nirenberg-Sobolev type.
Fichier principal
Vignette du fichier
DT-14-hal.pdf (296.12 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00634852 , version 1 (24-10-2011)
hal-00634852 , version 2 (11-07-2012)

Identifiants

Citer

Jean Dolbeault, Giuseppe Toscani. Improved Sobolev's inequalities, relative entropy and fast diffusion equations. 2011. ⟨hal-00634852v1⟩
155 Consultations
144 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More