Calculus of Variations and Geometric Measure Theory
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A. Figalli

A geometric lower bound on Grad's number

created by figalli on 26 Feb 2008
modified on 23 Apr 2008


Accepted Paper

Inserted: 26 feb 2008
Last Updated: 23 apr 2008

Journal: ESAIM Control Optim. Calc. Var.
Year: 2008


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


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