We establish Calder\'on \& Zygmund type estimates for a class of parabolic problems whose model is the non-homogeneous, degenerate/singular parabolic $p$-Laplacan system $$u_t - div \ (|Du|^{p-2}Du) = div \ (|F|^{p-2}F)\;,$$ proving that $$F \in L_{\loc} ^{ q} \Longrightarrow Du\in L^{q}_{\loc} \qquad \forall \ q\geq p\;.$$ We also treat systems with discontinuous coefficients of vanishing mean oscillation (VMO) type.

Gradient estimates for a class of parabolic systems / ACERBI E; MINGIONE G.. - In: DUKE MATHEMATICAL JOURNAL. - ISSN 0012-7094. - 136(2007), pp. 285-320.

### Gradient estimates for a class of parabolic systems

#### Abstract

We establish Calder\'on \& Zygmund type estimates for a class of parabolic problems whose model is the non-homogeneous, degenerate/singular parabolic $p$-Laplacan system $$u_t - div \ (|Du|^{p-2}Du) = div \ (|F|^{p-2}F)\;,$$ proving that $$F \in L_{\loc} ^{ q} \Longrightarrow Du\in L^{q}_{\loc} \qquad \forall \ q\geq p\;.$$ We also treat systems with discontinuous coefficients of vanishing mean oscillation (VMO) type.
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Gradient estimates for a class of parabolic systems / ACERBI E; MINGIONE G.. - In: DUKE MATHEMATICAL JOURNAL. - ISSN 0012-7094. - 136(2007), pp. 285-320.
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