The weak Harnack inequality and the rigidity of the anisotropic Trudinger's equation

Abstract

We prove a local weak Harnack inequality for nonnegative weak super-solutions to the anisotropic Trudinger equation. As an application, we show a proof of the Harnack inequality that bypasses any sort of Krylov-Safonov covering argument. We further develop an analysis of global sub-potential lower bounds which ultimately leads to the identification of a Barenblatt-type profile.