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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), Explicit constants in Harnack inequalities and regularity estimates, with an application to the fast diffusion equation. https://basepub.dauphine.fr/handle/123456789/21088

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02887013
Date
2020
Series title
Cahier de recherche du CEREMADE
Pages
55
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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)
This paper is devoted to the computation of various explicit constants in functional inequalities and regularity estimates for solutions of parabolic equations, which are not available from the literature. We provide new expressions and simplified proofs of the Harnack inequality and the corresponding Hölder continuity of the solution of a linear parabolic equation. We apply these results to the computation of a constructive estimate of a threshold time for the uniform convergence in relative error of the solution of the fast diffusion equation.
Subjects / Keywords
Moser's Harnack inequality; Intermediate asymptotics; Harnack Principle; Asymptotic behavior; Self-similar Barenblatt solutions; Stability; Entropy methods; Gagliardo-Nirenberg inequality; Fast diffusion equation; Rates of convergence