Global Calderon-Zygmund theory for parabolic p-Laplacian system: the case 1 < p ≤ 2n/n+2

摘要

The aim of this paper is to establish global Calderon- Zygmund theory to parabolic p -Laplacian system: u(t) - div(| del mu vertical bar(p-2) del u) = div(|F|Fp-2) in omega x (0, T) subset of Rn+1, proving that F is an element of L-q double right arrow del u is an element of L-q, for any q > max{p, n(2-p) 2 } and p > 1. Acerbi and Mingione [2] proved this estimate in the case p > 2n n+2 . In this article we settle the case 1 < p <= 2n n+2 . We also treat systems with discontinuous coefficients having small BMO (bounded mean oscillation) norm.

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