# A geometric lower bound on Grad’s number

ESAIM: Control, Optimisation and Calculus of Variations (2009)

- Volume: 15, Issue: 3, page 569-575
- ISSN: 1292-8119

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topFigalli, Alessio. "A geometric lower bound on Grad’s number." ESAIM: Control, Optimisation and Calculus of Variations 15.3 (2009): 569-575. <http://eudml.org/doc/245334>.

@article{Figalli2009,

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

author = {Figalli, Alessio},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Grad’s number; Korn-type inequality; axisymmetry of the domain; trend to equilibrium for the Boltzmann equation; Grad's number},

language = {eng},

number = {3},

pages = {569-575},

publisher = {EDP-Sciences},

title = {A geometric lower bound on Grad’s number},

url = {http://eudml.org/doc/245334},

volume = {15},

year = {2009},

}

TY - JOUR

AU - Figalli, Alessio

TI - A geometric lower bound on Grad’s number

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2009

PB - EDP-Sciences

VL - 15

IS - 3

SP - 569

EP - 575

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

LA - eng

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

UR - http://eudml.org/doc/245334

ER -

## References

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- [2] L. Desvillettes and C. Villani, On a variant of Korn’s inequality arising in statistical mechanics. ESAIM: COCV 8 (2002) 603–619. Zbl1092.82032MR1932965
- [3] L. Desvillettes and C. Villani, On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation. Invent. Math. 159 (2005) 245–316. Zbl1162.82316MR2116276
- [4] A. Figalli, F. Maggi and A. Pratelli, A mass transportation approach to quantitative isoperimetric inequalities. Preprint (2007). Zbl1196.49033
- [5] C. Villani, Hypocoercivity. Memoirs Amer. Math. Soc. (to appear). Zbl1197.35004MR2562709
- [6] W.P. Ziemer, Weakly differentiable functions. Sobolev spaces and functions of bounded variation. Graduate Texts in Mathematics 120. Springer-Verlag, New York (1989). Zbl0692.46022MR1014685

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