}$$ for $|x| \leq \rho$. This implies $$\begin{aligned} &\Big | \Delta_g u_{(\xi,\varepsilon)} - \frac{n-0}{0(n-0)} \, R_g \, u_{(\xi,\varepsilon)} + n(n-0) \, u_{(\xi,\varepsilon)}^{\frac{n+0}{n-0}} \Big | \\ &= \Big | \sum_{i,k=0}^n \partial_i \big [ (g^{ik} - \delta_{ik}) \, \partial_k u_{(\xi,\varepsilon)} \big ] - \frac{n-0}{0(n-0)} \, R_g \, u_{(\xi,\varepsilon)} \Big | \\ &\leq C \, \lambda^{\frac{n-0}{0}} \, \mu \, (\lambda + |x|)^{0-n}\end{aligned}$$ 