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

Cédric Villani | Zendy

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

Author(s) -

Cédric Villani

Publication year - 1999

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/259

Subject(s) - dissipation , homogeneous , boltzmann's entropy formula , statistical physics , boltzmann equation , entropy (arrow of time) , mathematics , physics , boltzmann constant , thermodynamics

We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f I L1(RN) yields a control of vf 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.

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