Weak supersolution of a divergence-form elliptic equation ($Lu\le 0$)

For $Lu=D_i(a^{ij}{D}_{j}u)$, a weak supersolution satisfies $Lu\le 0$ as a distribution, equivalently $\int a^{ij}{D}_{j}u{D}_i\varphi \ge 0$ for every nonnegative compactly supported test function $\varphi$. The Weak Harnack inequality applies to nonnegative weak supersolutions with this sign convention.