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.
@article{ASNSP_2012_5_11_4_843_0,
author = {Silvestre, Luis},
title = {H\"older estimates for advection fractional-diffusion equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {843--855},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 11},
number = {4},
year = {2012},
mrnumber = {3060702},
zbl = {1263.35056},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2012_5_11_4_843_0/}
}
TY - JOUR AU - Silvestre, Luis TI - Hölder estimates for advection fractional-diffusion equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 843 EP - 855 VL - 11 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2012_5_11_4_843_0/ LA - en ID - ASNSP_2012_5_11_4_843_0 ER -
%0 Journal Article %A Silvestre, Luis %T Hölder estimates for advection fractional-diffusion equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 843-855 %V 11 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2012_5_11_4_843_0/ %G en %F ASNSP_2012_5_11_4_843_0
Silvestre, Luis. Hölder estimates for advection fractional-diffusion equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 4, pp. 843-855. http://www.numdam.org/item/ASNSP_2012_5_11_4_843_0/
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