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On the differentiability of the solution to the Hamilton–Jacobi equation with critical fractional diffusion
Authors:Luis Silvestre
Institution:University of Chicago, Department of Mathematics, 5734 S. University Avenue, Chicago, United States
Abstract: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 C1,α solutions. The proof is achieved using a new Hölder estimate for solutions of advection–diffusion equations of order one with bounded vector fields that are not necessarily divergence free.
Keywords:Hamilton&ndash  Jacobi equation  Fractional diffusion
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