
Stability in Gagliardo-Nirenberg inequalities
Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2020), Stability in Gagliardo-Nirenberg inequalities. https://basepub.dauphine.fr/handle/123456789/21087
View/ Open
Type
Document de travail / Working paperExternal document link
https://hal.archives-ouvertes.fr/hal-02887010Date
2020Series title
Cahier de recherche CEREMADEPages
52
Metadata
Show full item recordAuthor(s)
Bonforte, MatteoDepartamento de Matemáticas
Dolbeault, Jean

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Nazaret, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]
Simonov, Nikita
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
The purpose of this paper is to establish a quantitative and constructive stability result for a class of subcritical Gagliardo-Nirenberg inequalities. We develop a new strategy, in which the flow of the fast diffusion equation is used as a tool: a stability result in the inequality is equivalent to an improved rate of convergence to equilibrium for the flow. In both cases, the tail behaviour plays a key role. The regularity properties of the parabolic flow allow us to connect an improved entropy-entropy production inequality during the initial time layer to spectral properties of a suitable linearized problem which is relevant for the asymp-totic time layer. Altogether, the stability in the inequalities is measured by a deficit which controls in strong norms the distance to the manifold of optimal functions.Subjects / Keywords
Stability; Entropy methods; Harnack Principle; Gagliardo-Nirenberg inequality; Fast diffusion equation; Asymptotic behavior; Self-similar Barenblatt so-lutions; Rates of convergence; Spectral gap; Hardy-Poincaré inequalities; Intermediate asymptoticsRelated items
Showing items related by title and author.
-
Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2022) Document de travail / Working paper
-
Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2023) Article accepté pour publication ou publié
-
Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2020) Document de travail / Working paper
-
Bonforte, Matteo; Dolbeault, Jean; Muratori, Matteo; Nazaret, Bruno (2017) Article accepté pour publication ou publié
-
Dolbeault, Jean; Toscani, Giuseppe (2016) Article accepté pour publication ou publié