Very weak solutions of subquadratic parabolic systems with non-standard p(x,t)-growth

The aim of this paper is to establish a higher integrability result for very weak solutions of certain parabolic systems whose model is the parabolic p(x,t)-Laplacian system. Under assumptions on the exponent function p : Omega(T) = Omega x (0,T) -> (2n/n+2, 2], it is shown that any very weak solution u : Omega(T) -> R-N with vertical bar Du vertical bar(p(.)(1-epsilon)) is an element of L-1(Omega(T)) belongs to the natural energy spaces, i.e. vertical bar Du vertical bar(P(.)) is an element of L-loc(1) (Omega(T)), provided epsilon > 0 is small enough. This extends the main result of Bogelein and Li (2014) to the subquadratic case. (C) 2017 Elsevier Ltd. All rights reserved.