Global Calderón–Zygmund theory for parabolic p-Laplacian system: the case [formula omitted

Abstract

The aim of this paper is to establish global Calderón–Zygmund theory to parabolic p-Laplacian system:ut−div(|∇u|p−2∇u)=div(|F|p−2F)inΩ×(0,T)⊂Rn+1, proving thatF∈Lq⇒∇u∈Lq, for any q>max⁡{p,n(2−p)2} and p>1. Acerbi and Mingione [2] proved this estimate in the case p>2nn+2. In this article we settle the case 1<p≤2nn+2. We also treat systems with discontinuous coefficients having small BMO (bounded mean oscillation) norm.