ESAIM: COCV
DOI: 10.1051/cocv:2008032

A geometric lower bound on Grad's number

Alessio Figalli

Université de Nice-Sophia Antipolis, Laboratoire J.-A. Dieudonné, UMR 6621, Parc Valrose, 06108 Nice Cedex 02, France; figalli@unice.fr

(Received January 13, 2008. Published online April 26, 2008.)

Abstract
In this note we provide a new geometric lower bound on the so-called Grad's number of a domain in terms of how far is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.

Mathematics Subject Classification. 49Q20, 49J40

Key words: Grad's number, Korn-type inequality, axisymmetry of the domain, trend to equilibrium for the Boltzmann equation


© EDP Sciences, SMAI 2008