On the differentiability of the solution to an equation with drift and fractional diffusion
Luís Silvestre · Indiana University Mathematics Journal · 2012
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 Holder continuity of the solutions, we prove that the solution becomes immediately differentiable with Holder continuous derivatives. Therefore, the solutions to the equation are classical.