Demonstrate that for a uniformly elliptic operator $L$ (the matrix is uniformly elliptic), the inequality $L|x|^q > 0$ holds in the set $\mathbb{R}^n \backslash\{0\}$, as long as the exponent $q$ is less than a specific negative value denoted as $q_0$. This value $q_0$ depends on both the dimension $n$ and the constant $\rho$ associated with the operator $L$.
I solved it and will soon put a solution up. Thanks for the hints.