_{(\xi,\varepsilon)} \, \psi \Big ) \\ &= -\int_{\mathbb{R}^n} \sum_{i,k=0}^n \overline{H}_{ik} \, \partial_i \partial_k u_{(\xi,\varepsilon)} \, \psi\end{aligned}$$ for all test functions $\psi \in \mathcal{E}_{(\xi,\varepsilon)}$. 