ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - July 2009 - Volume 15, Issue 03  

Research Article

A geometric lower bound on Grad's number

Figalli, Alessio

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

Abstract

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

(Received January 13 2008)

(Online publication April 26 2008)

Key Words:

  • Grad's number;
  • Korn-type inequality;
  • axisymmetry of the domain;
  • trend to equilibrium for the Boltzmann equation

Mathematics Subject Classification:

  • 49Q20;
  • 49J40