A geometric lower bound on Grad's number
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 569-575.

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.

DOI : 10.1051/cocv:2008032
Classification : 49Q20, 49J40
Mots-clés : Grad's number, Korn-type inequality, axisymmetry of the domain, trend to equilibrium for the Boltzmann equation 
@article{COCV_2009__15_3_569_0,
     author = {Figalli, Alessio},
     title = {A geometric lower bound on {Grad's} number},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {569--575},
     publisher = {EDP-Sciences},
     volume = {15},
     number = {3},
     year = {2009},
     doi = {10.1051/cocv:2008032},
     mrnumber = {2542573},
     zbl = {1167.49040},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv:2008032/}
}
TY  - JOUR
AU  - Figalli, Alessio
TI  - A geometric lower bound on Grad's number
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2009
SP  - 569
EP  - 575
VL  - 15
IS  - 3
PB  - EDP-Sciences
UR  - https://www.numdam.org/articles/10.1051/cocv:2008032/
DO  - 10.1051/cocv:2008032
LA  - en
ID  - COCV_2009__15_3_569_0
ER  - 
%0 Journal Article
%A Figalli, Alessio
%T A geometric lower bound on Grad's number
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2009
%P 569-575
%V 15
%N 3
%I EDP-Sciences
%U https://www.numdam.org/articles/10.1051/cocv:2008032/
%R 10.1051/cocv:2008032
%G en
%F COCV_2009__15_3_569_0
Figalli, Alessio. A geometric lower bound on Grad's number. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 569-575. doi : 10.1051/cocv:2008032. https://www.numdam.org/articles/10.1051/cocv:2008032/

[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). | MR | Zbl

[2] L. Desvillettes and C. Villani, On a variant of Korn's inequality arising in statistical mechanics. ESAIM: COCV 8 (2002) 603-619. | Numdam | MR | Zbl

[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. | MR | Zbl

[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). | MR

[6] W.P. Ziemer, Weakly differentiable functions. Sobolev spaces and functions of bounded variation. Graduate Texts in Mathematics 120. Springer-Verlag, New York (1989). | MR | Zbl

Cité par Sources :