On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion

Details On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion

2009-11-26

arxiv.org/abs/0911.5147v2

Mathematics

Analysis of PDEs

Scientific paper

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.

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