Global integrability and weak Harnack estimates for elliptic PDEs in divergence form

We show that two classically known properties of positive supersolutions uniformly elliptic PDEs, the boundary point principle (Hopf lemma) and global integrability, can be quantified with respect to each other. obtain an extension de Giorgi-Moser weak Harnack inequality, optimal norms involved, for equations in divergence form.