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