On the differentiability of the solution to an equation with drift and fractional diffusion Luis Silvestre 35B6535R1135K99fractional diffusiondrift-diffusion We consider an equation with drift and either critical or supercritical fractional diffusion. Under a regularity assumption for the vector field that is marginally stronger than what is required for H\"older continuity of the solutions, we prove that the solution becomes immediately differentiable with H\"older continuous derivatives. Therefore, the solutions to the equation are classical. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4568 10.1512/iumj.2012.61.4568 en Indiana Univ. Math. J. 61 (2012) 557 - 584 state-of-the-art mathematics http://iumj.org/access/