Calculus of Variations and Geometric Measure Theory
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E. Acerbi - G. Mingione

Gradient estimates for a class of parabolic systems

created by mingione on 29 Sep 2012

[BibTeX]

Published Paper

Inserted: 29 sep 2012
Last Updated: 29 sep 2012

Journal: Duke Math. J.
Volume: 136
Pages: 285-320
Year: 2007

Abstract:

We establish local Calderon & Zygmund type estimates for a class of parabolic problems whose model is the non-homogeneous, degeneratesingular parabolic $p$-Laplacean system \[u_t -\mbox{div}\ (
Du
^{p-2}Du) =\mbox{div}\ (
F
^{p-2}F)\] proving that \[ F \in L_{\mbox{loc}} ^{ q} \Longrightarrow Du\in L^{q}_{\mbox{loc}} \qquad \forall \ q\geq p.\] We also treat systems with discontinuous coefficients of VMO type.

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