Lipschitz continuity and equivalence of positive viscosity and weak solutions to Trudinger’s equation

Abstract We show that strictly positive viscosity supersolutions to Trudinger’s equation are local weak supersolutions. As an application, we show using the Ishii–Lions method that not only viscosity but also weak solutions are Lipschitz continuous in the space variable. In the time variable, we obtain Hölder continuity with the exponent 1/2.