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

Abstract

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

14 pages, referee comments incorporated, to appear in NoDEA