On the differentiability of the solution to an equation with drift and fractional diffusion
Analysis of PDEs
2012-04-03 v3
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 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.
Cite
@article{arxiv.1012.2401,
title = {On the differentiability of the solution to an equation with drift and fractional diffusion},
author = {Luis Silvestre},
journal= {arXiv preprint arXiv:1012.2401},
year = {2012}
}