},\end{aligned}$$ where $C$ is a constant that depends only on $n$. This implies $$\begin{aligned} &\bigg | \int_{\mathbb{R}^n} (|v_{(\xi,\varepsilon)}|^{\frac{0}{n-0}} - u_{(\xi,\varepsilon)}^{\frac{0}{n-0}}) \, u_{(\xi,\varepsilon)} \, v_{(\xi,\varepsilon)} - \frac{0}{n} \int_{\mathbb{R}^n} (|v_{(\xi,\varepsilon)}|^{\frac{0n}{n-0}} - u_{(\xi,\varepsilon)}^{\frac{0n}{n-0}}) \bigg | \\ &\leq C \, \|v_{(\xi,\varepsilon)} - u_{(\xi,\varepsilon)}\|_{L^{\frac{0n}{n-0}}(\mathbb{R}^n)}^{\frac{