Enlarging the functional space of decay estimates on semigroups

Clément Mouhot (1, 2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 DAMTP - Department of Applied Mathematics and Theoretical Physics

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]).

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Clément Mouhot. Enlarging the functional space of decay estimates on semigroups. 2010. ⟨hal-00440119v2⟩