What question did this study set out to answer?

The research aims to establish a relationship between viscosity and weak solutions of Trudinger’s equation, focusing on their continuity properties.

February 20, 2026Open Access

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

Key Points

The research aims to establish a relationship between viscosity and weak solutions of Trudinger’s equation, focusing on their continuity properties.
Demonstrating the equivalence of viscosity and weak solutions
Applying the Ishii–Lions method to analyze continuity
Assessing Lipschitz continuity in the space variable
Evaluating Hölder continuity in the time variable
Positive viscosity supersolutions are confirmed to be local weak supersolutions
Weak solutions are shown to be Lipschitz continuous in the space variable
Hölder continuity is obtained with an exponent of 1/2 in the time variable

Abstract

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.

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