Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off.

Cédric Villani

Revista Matemática Iberoamericana (1999)

  • Volume: 15, Issue: 2, page 335-351
  • ISSN: 0213-2230

Abstract

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We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f ∈ L1(RN) yields a control of √f in Sobolev norms as soon as f is locally bounded below. Under this additional assumption of lower bound, our result is an improvement of a recent estimate given by P.-L. Lions, and is optimal in a certain sense.

How to cite

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Villani, Cédric. "Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off.." Revista Matemática Iberoamericana 15.2 (1999): 335-351. <http://eudml.org/doc/39571>.

@article{Villani1999,
abstract = {We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f ∈ L1(RN) yields a control of √f in Sobolev norms as soon as f is locally bounded below. Under this additional assumption of lower bound, our result is an improvement of a recent estimate given by P.-L. Lions, and is optimal in a certain sense.},
author = {Villani, Cédric},
journal = {Revista Matemática Iberoamericana},
keywords = {Espacios LP; Entropía; Ecuaciones diferenciales en derivadas parciales; regularity estimates; entropy dissipation; Boltzmann equation; kinetic theory of gases; Boltzmann collision operator},
language = {eng},
number = {2},
pages = {335-351},
title = {Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off.},
url = {http://eudml.org/doc/39571},
volume = {15},
year = {1999},
}

TY - JOUR
AU - Villani, Cédric
TI - Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off.
JO - Revista Matemática Iberoamericana
PY - 1999
VL - 15
IS - 2
SP - 335
EP - 351
AB - We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f ∈ L1(RN) yields a control of √f in Sobolev norms as soon as f is locally bounded below. Under this additional assumption of lower bound, our result is an improvement of a recent estimate given by P.-L. Lions, and is optimal in a certain sense.
LA - eng
KW - Espacios LP; Entropía; Ecuaciones diferenciales en derivadas parciales; regularity estimates; entropy dissipation; Boltzmann equation; kinetic theory of gases; Boltzmann collision operator
UR - http://eudml.org/doc/39571
ER -

Citations in EuDML Documents

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  1. Radjesvarane Alexandre, Around 3D Boltzmann non linear operator without angular cutoff, a new formulation
  2. Radjesvarane Alexandre, Around 3D Boltzmann non linear operator without angular cutoff, a new formulation
  3. Laurent Desvillettes, Clément Mouhot, About L p estimates for the spatially homogeneous Boltzmann equation
  4. R Alexandre, C Villani, On the Landau approximation in plasma physics
  5. Clément Mouhot, Quelques résultats d’hypocoercitivité en théorie cinétique collisionnelle

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