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

2010/12/10 by Luís Silvestre, Silvestre, Luis
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1012.2401

Abstract

We consider an equation with drift and either critical or supercritical\nfractional diffusion. Under a regularity assumption for the vector field that\nis marginally stronger than what is required for Holder continuity of the\nsolutions, we prove that the solution becomes immediately differentiable with\nHolder continuous derivatives. Therefore, the solutions to the equation are\nclassical.\n

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