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, Emilio Daniele Giovanni; Mingione, Giuseppe. - In: DUKE MATHEMATICAL JOURNAL. - ISSN 0012-7094. - 136:(2007), pp. 285-320.
Gradient estimates for a class of parabolic systems
ACERBI, Emilio Daniele Giovanni;MINGIONE, Giuseppe
2007-01-01
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.File in questo prodotto:
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