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A weak Harnack estimate for supersolutions to the porous medium equation. (English) Zbl 1413.35266

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.

MSC:

35K65 Degenerate parabolic equations
35B45 A priori estimates in context of PDEs
35K10 Second-order parabolic equations