A geometric lower bound on Grad’s number

Alessio Figalli

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

  • 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 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.

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 (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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  1. [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). Zbl0957.49001MR1857292
  2. [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. [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. [4] A. Figalli, F. Maggi and A. Pratelli, A mass transportation approach to quantitative isoperimetric inequalities. Preprint (2007). Zbl1196.49033
  5. [5] C. Villani, Hypocoercivity. Memoirs Amer. Math. Soc. (to appear). Zbl1197.35004MR2562709
  6. [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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