Higher integrability for singular doubly nonlinear systems.

We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is ∂ t | u | q - 1 u - div | D u | p - 2 D u = div | F | p - 2 F in Ω T : = Ω × ( 0 , T ) with parameters p > 1 and q > 0 and Ω ⊂ R n . In this paper, we are concerned with the ranges q > 1 and p > n ( q + 1 ) n + q + 1 . A key ingredient in the proof is an intrinsic geometry that takes both the solution u and its spatial gradient Du into account.