Self-improving property of degenerate parabolic equations of porous medium-type

We show that the gradient of solutions to degenerate parabolic equations of porous medium-type satisfies a reverse H"older inequality in suitable intrinsic cylinders. We modify the by-now classical Gehring lemma by introducing an intrinsic Calder'on-Zygmund covering argument, and we are able to prove local higher integrability of the gradient of a proper power of the solution $u$.