arXiv:1012.2401 Abstract | arXiv Analytics

arXiv:1012.2401 [math.AP]Abstract References Reviews Resources

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

Published 2010-12-10, updated 2012-03-30Version 3

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.

Categories: math.AP

Keywords: differentiability, regularity assumption, holder continuous derivatives, vector field, holder continuity

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