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.