• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

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
BDNS2020.pdf (604.1Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02887010
Date
2020
Series title
Cahier de recherche CEREMADE
Pages
52
Metadata
Show full item record
Author(s)
Bonforte, Matteo
Departamento de Matemáticas
Dolbeault, Jean cc
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 asymptotics

Related items

Showing items related by title and author.

  • Thumbnail
    Stability in Gagliardo-Nirenberg-Sobolev inequalities : flows, regularity and the entropy method 
    Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2022) Document de travail / Working paper
  • Thumbnail
    Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations 
    Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2023) Article accepté pour publication ou publié
  • Thumbnail
    Explicit constants in Harnack inequalities and regularity estimates, with an application to the fast diffusion equation 
    Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2020) Document de travail / Working paper
  • Thumbnail
    Weighted fast diffusion equations (Part I): Sharp asymptotic rates without symmetry and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities 
    Bonforte, Matteo; Dolbeault, Jean; Muratori, Matteo; Nazaret, Bruno (2017) Article accepté pour publication ou publié
  • Thumbnail
    Stability results for logarithmic Sobolev and Gagliardo-Nirenberg inequalities 
    Dolbeault, Jean; Toscani, Giuseppe (2016) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo