# On a variant of Korn's inequality arising in statistical mechanics

L. Desvillettes; Cédric Villani

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 8, page 603-619
- ISSN: 1292-8119

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topDesvillettes, L., and Villani, Cédric. "On a variant of Korn's inequality arising in statistical mechanics." ESAIM: Control, Optimisation and Calculus of Variations 8 (2010): 603-619. <http://eudml.org/doc/90662>.

@article{Desvillettes2010,

abstract = {
We state and prove a Korn-like inequality for a vector field in a
bounded open set of $\mathbb\{R\}^N$, satisfying a tangency boundary condition.
This inequality, which is crucial in our study of the trend towards
equilibrium for dilute gases, holds true if and only if the domain is not
axisymmetric. We give quantitative, explicit estimates on how the
departure from axisymmetry affects the constants; a Monge–Kantorovich
minimization problem naturally arises in this process.
Variants in the axisymmetric case are briefly discussed.
},

author = {Desvillettes, L., Villani, Cédric},

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

keywords = {Korn's inequality; Boltzmann equation; Monge–Kantorovich mass transportation
problem.; Monge-Kantorovich mass transportation problem},

language = {eng},

month = {3},

pages = {603-619},

publisher = {EDP Sciences},

title = {On a variant of Korn's inequality arising in statistical mechanics},

url = {http://eudml.org/doc/90662},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Desvillettes, L.

AU - Villani, Cédric

TI - On a variant of Korn's inequality arising in statistical mechanics

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 8

SP - 603

EP - 619

AB -
We state and prove a Korn-like inequality for a vector field in a
bounded open set of $\mathbb{R}^N$, satisfying a tangency boundary condition.
This inequality, which is crucial in our study of the trend towards
equilibrium for dilute gases, holds true if and only if the domain is not
axisymmetric. We give quantitative, explicit estimates on how the
departure from axisymmetry affects the constants; a Monge–Kantorovich
minimization problem naturally arises in this process.
Variants in the axisymmetric case are briefly discussed.

LA - eng

KW - Korn's inequality; Boltzmann equation; Monge–Kantorovich mass transportation
problem.; Monge-Kantorovich mass transportation problem

UR - http://eudml.org/doc/90662

ER -

## References

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