Summability and existence results for nonlinear parabolic equations

In this paper we study the summability of the solutions and of their gradients for a class of nonlinear parabolic equations. We show how it is related to the summability of the datum ff which belongs to Lr(0,T;Lq(Ω))Lr(0,T;Lq(Ω)), r∈[1,+∞]r∈[1,+∞], q∈[1,+∞]q∈[1,+∞].