Hölder estimates for advection fractional-diffusion equations

Luis Silvestre ^[1]
1. [1] University of Chicago
  
  University of Chicago
  
  City of Chicago, Estados Unidos
Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 11, Nº 4, 2012, págs. 843-855
Idioma: inglés
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Resumen
- We analyse conditions for an evolution equation with a drift and fractional diffusion to have a Hölder continuous solution. In case the diffusion is of order one or more, we obtain Hölder estimates for the solution for any bounded drift. In the case when the diffusion is of order less than one, we require the drift to be a Hölder continuous vector ﬁeld in order to obtain the same type of regularity result.