Inserted: 26 feb 2008
Last Updated: 23 apr 2008
Journal: ESAIM Control Optim. Calc. Var.
In this note we provide a new geometric lower bound on the so-called Grad's number of a domain $\Omega$ in terms of how far $\Omega$ is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.
Keywords: Grad's number, Korn-type inequalities, axisymmetry of the domain, trend to equilibrium for the Boltzmann equation