(Proposition 4.2) Let $\varphi$ be a smooth solution to (1.1), (1.2). Then there exists $p_{n}>1$, depending only on $n$, and a constant $C$, depending on $||\varphi||_{0}$, $||F||_{0}$, $||n+\Delta\varphi||_{L^{p_{n}}(dvol_{g})}$, and the background metric $g$, such that