For any $1<p<\infty$, there exist constants $\tilde{C}(p)>0$, depending on $||\varphi||_{0}$, $||F||_{0}$, the background metric $g$(with dependence in a way described in Theorem 3.1) and $p$, such that $||n+\Delta\varphi||_{L^{p}}\leq\tilde{C}(p)$.