Calderón-Zygmund estimates for parabolic p-Laplacian systems with non-divergence form right-hand sides

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 \(L^{\mu s}\) $L^{\mu s}$ , where the exponent \(\mu \) $\mu$ depends explicitly on p, N, and a prescribed target exponent \(s>p\) $s>p$ , then the spatial gradient of the solution enjoys improved integrability \(Du \in L^s_\mathrm{{loc}}\) $Du\in L_{\mathrm{loc}}^s$ . 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.