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

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 $C^{1,\alpha }$ 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.

References in corpus (1)

• Regularity theory for fully nonlinear integro-differential equations

Cited by in corpus (4)

• $L^p$-maximal regularity of nonlocal parabolic equation and applications
• Heat kernel estimates for critical fractional diffusion operator
• Well-posedness of fully nonlinear and nonlocal critical parabolic equations
• Singular SDEs with critical non-local and non-symmetric Lévy type generator