article

Title: On the differentiability of the solution to an equation with drift and fractional diffusion

Authors: Luis Silvestre

Issue: Volume 61 (2012), Issue 2, 557-584

Abstract:

$We consider an equation with drift and either critical or supercritical fractional diffusion. Under a regularity assumption for the vector field that is marginally stronger than what is required for H\"older continuity of the solutions, we prove that the solution becomes immediately differentiable with H\"older continuous derivatives. Therefore, the solutions to the equation are classical.$