%0 Journal Article
%T On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion
%A Luis Silvestre
%J Mathematics
%D 2009
%I arXiv
%X We prove that the Hamilton Jacobi equation for an arbitrary Hamiltonian $H$ (locally Lipschitz but not necessarily convex) and fractional diffusion of order one (critical) has classical $C^{1,\alpha}$ solutions. The proof is achieved using a new H\"older estimate for solutions of advection diffusion equations of order one with bounded vector fields that are not necessarily divergence free.
%U http://arxiv.org/abs/0911.5147v2