Gradient Holder regularity for parabolic normalized p(x,t)-Laplace equation

We consider interior H"{o}lder regularity of the spatial gradient of viscosity solutions to the normalized $p(x,t)$-Laplace equation $$u_t=({\delta }_{ij}+(p(x,t)-2)\frac{u_i{u}_j}{\mathrm{\mid }Du{\mathrm{\mid }}^2})u_{ij}$$ with some suitable assumptions on $p(x,t)$, which arises naturally from a two-player zero-sum stochastic differential game with probabilities depending on space and time.