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

Revista Matemática Iberoamericana (1999)

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

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topVillani, 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 -

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