A control problem related to the parabolic dominative $p$-Laplace equation

We show that value functions of a certain time-dependent control problem in $\mathrm{\Omega }\times (0,T)$, with a continuous payoff $F$ on the parabolic boundary, converge uniformly to the viscosity solution of the parabolic dominative $p$-Laplace equation $$2(n+p)u_t=\mathrm{\Delta }u+(p-2){\lambda }_n(D^{2}u),$$ with the boundary data $F$. Here $2\le p<\mathrm{\infty }$, and ${\lambda }_n(D^{2}u)$ is the largest eigenvalue of the Hessian $D^{2}u$.