I would like to know whether viscosity solutions to $u_{t} - F( D^{2} (u) ) = 0$ are $C^{1, \alpha}$ analogous to the elliptic case as in the book by Caffarelli and Cabre .

Here F is assumed to be uniformly elliptic .

$D^{2}(u)$ is the spatial Hessian of $u$.

An answer would be appreciated.