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

top
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

top

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

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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.