A weak Harnack estimate for supersolutions to the porous medium equation. (Q1686823)

The Author proves a weak Harnack estimate for the weak supersolutions to the porous medium equation (PME). Properties of supersolutions to the PME were considered in several recent papers. However, it is difficult to find a reference with a complete proof of the weak Harnack estimate for the weak supersolutions. The purpose of this work is to present a proof for the weak Harnack estimate in full detail. The proof follows the same pattern of the weak Harnack estimate for the weak supersolutions to the \(p\)-Laplacean and it is based on a priori estimates for the supersolutions and measure theoretical arguments.