is elliptic of order $m$, meaning that its homogeneous principal part $P_m$ satisfies $P_m(\xi) \neq 0$ for every $\xi \in \mathbb{R}^n \setminus \{0\}$.
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For every $r \in \mathbb{R}$ and every pair of cutoff functions $\chi, \chi_1 \in C_c^\infty(\mathbb{R}^n)$ such that $\chi_1 = 1$ on an open neighbourhood of $\operatorname{supp}\chi$, there exists a constant $C = C(P,r,\chi,\chi_1) > 0$ such that every distribution $u \in \mathcal{S}'(\mathbb{R}^n)$ satisfying