
Flows and functional inequalities for fractional operators
Dolbeault, Jean; Zhang, An (2017), Flows and functional inequalities for fractional operators, Applicable Analysis, 96, 9, p. 1547-1560. 10.1080/00036811.2017.1286647
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Type
Article accepté pour publication ou publiéDate
2017Nom de la revue
Applicable AnalysisVolume
96Numéro
9Éditeur
Gordon and Breach
Pages
1547-1560
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This paper collects results concerning global rates and large time asymptotics of a fractional fast diffusion on the Euclidean space, which is deeply related with a family of fractional Gagliardo-Nirenberg-Sobolev inequalities. Generically, self-similar solutions are not optimal for the Gagliardo-Nirenberg-Sobolev inequalities, in strong contrast with usual standard fast diffusion equations based on non-fractional operators. Various aspects of the stability of the self-similar solutions and of the entropy methods like carré du champ and Rényi entropy powers methods are investigated and raise a number of open problems.Mots-clés
self-similar variables; Rényi entropy powers; carré du champ; fractional Gagliardo-Nirenberg-Sobolev inequality; fractional Sobolev inequality; fractional fast diffusion equation; self-similar solutions; asymptotic behavior; intermediate asymptotics; rate of convergence; entropy methods; entropy – entropy production inequalityPublications associées
Affichage des éléments liés par titre et auteur.
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Dolbeault, Jean; Zhang, An (2016) Article accepté pour publication ou publié
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Dolbeault, Jean (2021) Article accepté pour publication ou publié
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Loss, Michael; Esteban, Maria J.; Dolbeault, Jean (2012) Article accepté pour publication ou publié
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Esteban, Maria J. (2017) Chapitre d'ouvrage
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Esteban, Maria J.; Dolbeault, Jean; Bosi, Roberta (2008) Article accepté pour publication ou publié