Fractional operators with singular drift: smoothing properties and Morrey–Campanato spaces

• Diego Chamorro ^[1] ; Stéphane Menozzi ^[1]
  1. [1] University of Évry Val d'Essonne

     University of Évry Val d'Essonne

     Arrondissement d'Évry, Francia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 4, 2016, págs. 1445-1499
• Idioma: inglés
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• Resumen

  • We investigate some smoothness properties for a linear transport-diffusion equation involving a class of non-degenerate Lévy type operators with singular drift. Our main argument is based on a duality method using the molecular decomposition of Hardy spaces through which we derive some Hölder continuity for the associated parabolic PDE. This property will be fulfilled as far as the singular drift belongs to a suitable Morrey–Campanato space for which the regularizing properties of the Lévy operator suffice to obtain global Hölder continuity.