Abstract We establish local Calderón-Zygmund type estimates for weak solutions to nonlinear parabolic systems with p -growth and VMO coefficients. In particular, we prove that if the right-hand side belongs locally to L^ s L μ s, where the exponent μ depends explicitly on p, N, and a prescribed target exponent s>p s > p, then the spatial gradient of the solution enjoys improved integrability Du Lˢ₋₎₂ D u ∈ L loc s. The result provides a sharp transfer of integrability from the data to the gradient, consistent with the natural parabolic scaling, and recovers the optimal exponents in the linear case p=2 p = 2. The proof combines intrinsic scaling techniques with a Calderón-Zygmund type iteration scheme.
Andrade et al. (Fri,) studied this question.