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Pré-Publication, Document De Travail Année : 2020

Stability in Gagliardo-Nirenberg inequalities

Résumé

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.
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Dates et versions

hal-02887010 , version 1 (01-07-2020)
hal-02887010 , version 2 (29-04-2021)
hal-02887010 , version 3 (27-05-2022)

Identifiants

Citer

Matteo Bonforte, Jean Dolbeault, Bruno Nazaret, Nikita Simonov. Stability in Gagliardo-Nirenberg inequalities. 2020. ⟨hal-02887010v1⟩
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