Let the assumptions and notations be as above. Then we have in all three cases listed in (2)

$$\sup_{X}|u_{t}-v_{t}|\leq C\|e^{f}-e^{h}\|_{L^{1}}^{1/(n+3+\sigma_{a})},$$

(2.3)

where in each case, $\sigma_{a}>0$ is the power of $r$ in $\gamma_{a}(r)$, i.e. $\gamma_{a}(r)=r^{\sigma_{a}}$, and $C$ is a constant depending only on $n,k,\omega,\chi$, $K>0$ and $p_{a}$.