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Enlarging the functional space of decay estimates on semigroups

Mouhot, Clément (2010), Enlarging the functional space of decay estimates on semigroups. https://basepub.dauphine.fr/handle/123456789/17337

Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-00440119/
Date
2010
Publisher
Université Paris-Dauphine
Series title
Cahier de recherche du CEREMADE
Published in
Paris
Pages
7
Metadata
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Author(s)
Mouhot, Clément
Abstract (EN)
This note briefly presents a new method for enlarging the functional space of a ``spectral-gap-like'' estimate of exponential decay on a semigroup. A particular case of the method was first devised in hal-00076709 for the spatially homogeneous Boltzmann equation, and a variant was used in Ref. hal-00124876 in the same context for inelastic collisions. We present a generalized abstract version of it, a short proof of the algebraic core of the method, and a new application to the Fokker-Planck equation. More details and other applications shall be found in the work in preparation Ref. [3] (another application to quantum kinetic theory can be found in the work in preparation Ref. [4]).
Subjects / Keywords
spectral gap; exponential decay; semigroup; Fokker-Planck equation; Poincaré inequality