# A geometric lower bound on Grad's number

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- 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 (2008): 569-575. <http://eudml.org/doc/90927>.

@article{Figalli2008,

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.
},

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},

language = {eng},

month = {4},

number = {3},

pages = {569-575},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/90927},

volume = {15},

year = {2008},

}

TY - JOUR

AU - Figalli, Alessio

TI - A geometric lower bound on Grad's number

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/4//

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 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.

LA - eng

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

UR - http://eudml.org/doc/90927

ER -

## References

top- L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. The Clarendon Press, Oxford University Press, New York (2000).
- L. Desvillettes and C. Villani, On a variant of Korn's inequality arising in statistical mechanics. ESAIM: COCV8 (2002) 603–619.
- 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.
- A. Figalli, F. Maggi and A. Pratelli, A mass transportation approach to quantitative isoperimetric inequalities. Preprint (2007).
- C. Villani, Hypocoercivity. Memoirs Amer. Math. Soc. (to appear).
- W.P. Ziemer, Weakly differentiable functions. Sobolev spaces and functions of bounded variation. Graduate Texts in Mathematics 120. Springer-Verlag, New York (1989).

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