Gradient estimates for a class of parabolic systems

Abstract

We establish local Calderón-Zygmund-type estimates for a class of parabolic problems whose model is the nonhomogeneous, degenerate/singular parabolic $p$-Laplacian system $u_t-\mathrm{div}(|\mathrm{Du}|{}^{p-2}\mathrm{Du})=\mathrm{div}(|F|{}^{p-2}F),$ proving that $F\in L_{}{\mathrm{loc}}^q\Rightarrow \mathrm{Du}\in L_{}^q\mathrm{loc},\hspace{1em}\forall \hspace{0.17em}q\ge p.$ We also treat systems with discontinuous coefficients of vanishing mean oscillation (VMO) type