We are interested in existence and regularity results for weak solutions of parabolic equations of the type ∂tu − div a(x, t, Du) = 0 on a parabolic space time cylinder T . The vector field a is assumed to satisfy a non-standard p, q-growth condition. We treat the subquadratic case, where 2n/n + 2 < p <2 and p ≤ q < p + 4/n + 2 holds. We show existence of weak su ∈ Lp…