Solution
= Solution
Positivity and continuity of $g$ give $\mu=\min_{[1/2,2]}g>0$ and a finite maximum $G$. Hence, for every $x$ in the shell and every $\xi\in\mathbb R^3$,
$$
\boxed{\lambda|\xi|^2\le\xi^TA(x)\xi\le\Lambda|\xi|^2,\qquad \lambda=\min(1,\mu)>0,\quad\Lambda=\max(1,G).}
$$
This is the <uniformly elliptic operator> condition. Positivity at separate points without a compactness/continuity lower bound would not alone supply a common ellipticity constant.