A geometric lower bound on Grad's number

Alessio Figalli

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

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

Abstract

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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.

How to cite

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Figalli, 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

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  1. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. The Clarendon Press, Oxford University Press, New York (2000).  
  2. L. Desvillettes and C. Villani, On a variant of Korn's inequality arising in statistical mechanics. ESAIM: COCV8 (2002) 603–619.  
  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.  
  4. A. Figalli, F. Maggi and A. Pratelli, A mass transportation approach to quantitative isoperimetric inequalities. Preprint (2007).  
  5. C. Villani, Hypocoercivity. Memoirs Amer. Math. Soc. (to appear).  
  6. 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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