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

• Autores: Cédric Villani
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 15, Nº 2, 1999, págs. 335-352
• Idioma: inglés
• Títulos paralelos:
  • Cálculos de regularidad vía la disipación de entropía para la ecuación de Boltzmann espacialmente homogénea sin tope.
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• Resumen

  • We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f Î 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.