Higher integrability for doubly nonlinear parabolic systems.

In this paper we establish a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The proof is based on a new intrinsic scaling that involves both the solution and its spatial gradient. It allows to compensate for the different scaling of the system in | u | and | Du |. The result covers the range of parameters p > 2 n n + 2 and 0 < q ≤ 1 .