A reverse Holder inequality for the gradient of solutions to Trudinger's equation

Abstrakt

We provide a higher integrability result for the gradient of positive solutions to Trudinger's equation (also known as the doubly nonlinear equation) for the range p is an element of [2, infinity). The estimate is achieved by refining a construction of intrinsic cylinders from the vectorial setting by incorporating estimates that are only available in the scalar case.

Klíčová slova

• Trudinger's equation
• Reverse Holder inequality
• p-Laplacian
• Gehring's lemma